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Module.2.study.guide.part4

Course: BIO BIOL 1510, Fall 2007
School: Georgia Tech
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1510 Biology Module #2 Part 4 Page 1 of 9 Book: Chapter 53: 53.1 53.4 Pages 1159 1178 September 26, 2007 53.1 Communities interactions include competition, predation, herbivory, symbiosis (parasitism, mutualism, and commensalisms), and disease Interspecific interaction : interactions of one organism w/another species in the community interspecific competition occurs when species compete for a...

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1510 Biology Module #2 Part 4 Page 1 of 9 Book: Chapter 53: 53.1 53.4 Pages 1159 1178 September 26, 2007 53.1 Communities interactions include competition, predation, herbivory, symbiosis (parasitism, mutualism, and commensalisms), and disease Interspecific interaction : interactions of one organism w/another species in the community interspecific competition occurs when species compete for a particular resource that is in short supply strong competition can lead to a local elimination of one of the two competing species, a process called competitive exclusion competitive exclusion principle: o G. F. Gause two species competing for the same limiting resources cannot coexist in the same place Even slight reproductive advantage will eventually lead to local elimination of the inferior competitor Ecological niche : sum total of a species' use of the biotic and abiotic resources in its environment Resource partitioning : the differentiation of niches that enables similar species to coexist in a community Character displacement : tendency for characteristics to be more divergent in sympatric (geographically overlapping) populations of two species than in allopatric (geographically separate) populations of the same two species o Example: variation in beak sizes Galapagos finches Predation o Cryptic coloration : camouflage chemical defenses Batesian mimicry : when a palatable or harmless species mimics an unpalatable or harmful model Mullerian mimicry : two or more unpalatable species resemble each other; each species gains an additional advantage b/c the greater the number of unpalatable species Both predators and prey use mimicry o Aposematic coloration : bright warning coloration exhibited by animals w/effective o o o 53.2 Species diversity : the variety of different kinds of organisms that make up the community o Species richness : total number of different species in the community o Relative abundance : the proportion each species represents of the total individuals in the community Biology 1510 Module #2 Part 4 Page 2 of 9 Trophic structure : feeding relationships btwn organisms Food chain : The transfer of food energy up the trophic levels from its source in plants and other photosynthetic organisms (primary producers) through herbivores (primary consumers) to carnivores (secondary and tertiary consumers) and eventually to decomposers food webs : system of linked food chains food chains are generally short...why?...hypothesis: o energetic hypothesis : suggests that the length of a food chain is limited by the o inefficiency of energy transfer along the chain only around 10% of energy stored in the organic matter of each trophic lvl is converted to organic matter at the next level dynamic stability hypothesis : proposes that long food chains are less stable than short chains pop fluctuations at lower lvls are magnified at higher lvls top predators must be able to recover from environmental shocks that can reduce food supply o food chains shorter in unpredictable environments most data available supports energetic hypothesis certain species have an especially large impact on the structure of the entire communities either b/c they are highly abundant or b/c they play a pivotal role in community dynamics dominant species : those species in a community that are the most abundant or that collectively have the highest biomasstotal mass of all individuals in a population o exert a powerful control over the occurrence and distribution of other species o how do we get dominant species? Dominant species are most competitive in exploiting limited resources More successful at avoiding predation or the impact of disease This latter idea could explain the high biomass that invasive species (species, generally introduced by humans, that take hold outside their native range) can attain in environments lacking their natural predators and pathogens Keystone species : in contrast to dominant species, not necessarily abundant in a community, but exert strong control on community structure not by numerical might but by their pivotal ecological roles, or niches Foundation species : Some organisms exert their influence not through their trophic interactions but by causing physical changes in the environment that affect the structure of the community. Such organisms may alter the environment through their behavior or by virtue of their large collective biomass. o Act as facilitators that have positive effects on the survival and reproduction of some of the other species in the community Bottomup model : postulates a unidirectional influence from lower to higher trophic lvls o In this case, the presence or absence of mineral nutrients (N ) controls plant (V ) numbers, which control herbivore (H ) numbers, which in turn control predator (P ) numbers. The simplified bottomup model is thus N V H P Biology 1510 Module #2 Part 4 Page 3 of 9 o To change need to alter biomass at lower lvls Topdown model : opposite of above o Trophic cascade model o N V H P Many intermediate models exist; interactions btwn lvls reciprocal Biomanipulation : alteration of communities' trophic lvls (by ppl) 53.3 Nonequilibrium model : describes communities as constantly changing after being buffeted by disturbances o Disturbance : event that changes a community, removes organisms from it, and alters resource availability not always negative, can create niche for other species intermediate disturbance hypothesis : suggests that moderate lvls of disturbance can create conditions that foster greater species diversity than low or high lvls of disturbance o high lvls create environmental stresses that exceed tolerance of many species low lvls allow for dominant species to out compete others ecological succession : process in which a disturbed area may be colonized bya variety of species, which are gradually replaces by other species, which are in turn replaces by still other species primary succession : when this process begins in a virtually lifeless area where soil has not yet formed, such as on a new volcanic island or on the rubble left behind by a retreating glacier o only life forms initially presentautotrophic prokaryotes secondary succession : occurs when an existing community has been cleared by some disturbance that leaves the soil intact o early species may facilitate or inhibit establishment of late species 53.4 2 factors correlated w/a community's species diversity: geographic location and size Equatorialpolar gradients: o Darwin and Wallace both noted that tropical habitats support many more species than do temperate and polar regions: 2 factors for this: Evolutionary history Tropical communities generally older than temperate or polar communities Biology 1510 Module #2 Part 4 Page 4 of 9 Climate: o More time for speciation 2 main climatic factors correlated w/biodiversity are solar energy input and water availabilityconsidered together by measuring a community's rate of evapotranspiration, the evaporation of water from soil plus the transpiration of water from plants o Much higher in hot areas Speciesarea curve (Alexander von Humbolt/1807): quantifies what probably seems obvious: all other factors being equal, the larger the geographic area of a community, the greater the number of species Island equilibrium model o 2 factors determine # of species that will eventually inhabit an island: 1) rate at which new species immigrate to island 2) rate at which species become extinct on island At any given time, island's immigration and extinction rates are also affected by the number of species already present. As the number of species on the island increases, the immigration rate of new species decreases, because any individual reaching the island is less likely to represent a species that is not already present. At the same time, as more species inhabit an island, extinction rates on the island increase because of the greater likelihood of competitive exclusion. These relationships make up MacArthur and Wilson's model of studies of the diversity of plants and animals on many island chains Lecture: continued: Ecosystems October 1, 2007 3 areas being focused on for limiting resources: terrestrial, marine,, freshwater Limiting resources in oceans o Great depth=little light=less photosynthesis o Phosphate can be limiting o Most cases there is one limiting resource o Chlorophyllthere are algae at great depths...algae at greater depths have less chlorophyll than algae near surface Freshwater lakes: o Reason ppl though P was a limiting resource in ocean was b/c they observed P was a limiting resource in freshwater Fertilizers (farming) run down to lakes causes spike in growth wholelake Schindler's studies N not limiting P limiting Biology 1510 Module #2 Part 4 Page 5 of 9 o Lakes that are eutrophic (lots of resources)...high productivity, low species diversity, algae locks light to plants at bottom and not a lot of oxygen for fish...b/c competition decreases species diversity Fastest growing thing dominants b/c no limiting resources cytobacteria Ligatrophicless nutrients...not productive, but clear water and more diverse o species (lots of fish) pyramids of energy and biomass o total energy content or biomass varies w/trophic lvl The energy available to any trophic level depends on ecosystem NPP and the number and efficiency of trophic transfers involved. Many ecosystems show a "pyramid" structure, with energy content and biomass both decreasing with trophic level. Marine ecosystems often show an inverted pyramid of biomass. Material flow through ecosystems o C, N, P, and S all have important biologicallydriven steps in their global cycles o The time scale of different compartments may range from less than a year to millions of years Ocean: time scales of hundreds to thousands of yrs Atmosphere: time scale of months to yrs Continents: time scale up to many million of yrs Ecological efficiency: o Ee= P/(P+R+W) Assimilate: P+R Consumed: (P+R+W) PRS Q: Caterpillar Energy Efficiency Example o What is the ecological efficiency and production efficiency? Total energy: 200J; feces: 100J; growth: 33J; cellular respiration: 67J Ecological efficiency= 33J/200J= 17% Production efficiency = 67J/200J= 33% Water cycle: evaporationcloudsprecipitation o 97% of water in ocean o 2% in glaciers Carbon cycle: Ee=ecological efficiency (trophic) P=net production R=respiration W=waste Large reservoirs of C: fossil fuels and intermediate and deep waters Transitions: organisms pumping C back into atmosphere & and plants turning C to O Biology 1510 Module #2 Part 4 Page 6 of 9 Deforestation causes there to be more C in atmosphere...trees out of systemno longer able to fix C Where does C come from? Carbon Cycle Perturbations: fossil fuel combustion is adding CO2 to atmosphere at rate of 5 6 Pg C y1 Nitrogen Cycle Fixed by: o Marine organisms o Industrial process o Biological processes o People planting things N runs off in soil Highest productivity in runoff areas Many ecosystems are Nlimited Open ocean (many regions). o N availability regulates primary production of organic matter and the potential flux of organic C to the deep sea. o The biological pump moves organic C rapidly downward through the water column: zooplankton feed on phytoplankton and produce dense, rapidlysinking fecal pellets. o The N cycle acts as a regulator of the C cycle Book: Chapter 54: all Pages 11841206 October 1, 2007 54.1 Ecosystem ecology emphasizes energy flow and chemical cycling Primary producers<primary consumers (herbivores)<secondary consumers (carnivores)< tertiary consumers (carnivores) Biology 1510 Module #2 Part 4 Page 7 of 9 o Detrivores /decomposers: consumers that get their energy from detritus nonliving organic material Detrivores decompose the organic material in an ecosystem and transfer the chemical elements in inorganic forms to abiotic reservoirs such as soil, water, and air 54.2 Primary production : the amount of light energy converted to chemical energy (organic compounds) by autotrophs during a given time period Primary production in marine and freshwater ecosystems: o Light limitation Partially limits production in ocean, but not only factortropics are sometimes relatively unproductive even though they get the greatest amount of light Nutrient limitation o Limiting nutrient : element that must be added in order for production to increase in a particular area The nutrient most often limiting in marine envt is N or P Less abundant in photic zone, more abundant in deeper water Several large areas of the ocean, however, have low phytoplankton densities in spite of relatively high nitrogen concentrations. For example, the waters of the Sargasso Sea, a subtropical region of the Atlantic Ocean, are among the most transparent in the world because of their very low density of phytoplankton. A series of nutrient enrichment experiments revealed that in this case, it is availability of the micronutrient iron that limits primary production Why are iron concentrations naturally low in certain oceanic regions? Windblown dust from the land is the main process delivering iron to oceanlittle reaches central Pacific and central Atlantic Ocean Fe and N related where Fe is limiting, adding iron stimulates growth of cyanobacteria that fix N Primary production in terrestrial and wetland ecosystems: o Temp and moisture key factors Iron Cyanobacteria N fixation phytoplankton production Actual evapotranspiration : the annual amount of water transpired by plants and evaporated from a landscape o Increase in actual evapotranspiration= increase in primary production Mineral nutrients in soil also key limiting factor Increases w/amount of precipitation & amount of solar E Biology 1510 Module #2 Part 4 Page 8 of 9 54.3 Energy transfer btwn trophic lvls is usually less than 20% efficient o much of primary production not used by consumers Secondary production : the amount of chemical energy in consumers' food that is converted to their own new biomass during a given time period Production efficiency : fraction of energy stored in food that is not used for respiration o Production efficiency=(Net secondary production)/(Assimilation of primary production) Trophic efficiency : percentage of production transferred from one trophic lvl to the next o always less than production efficiency b/c they take into account not only energy lost through respiration and contained in feces, but also energy in organic material in a lower trophic lvl that is not consumed by the next trophic lvl o usually range from 520% loss of energy w/each transfer in a food chain can be represented by a pyramid of net production biomass pyramid each tier represents the standing crop (the total dry weight of all organism) in one trophic lvl o narrow at topcarnivores; big baseprimary producers o however, certain aquatic ecosystems have inverted biomass pyramids: primary consumers outweigh the producers occur b/c producers phytoplankton so quickly grow, reproduce, and are consumed by the zooplankton that they never develop a large population size, or standing crop phytoplankton have a short turnover timemeans they have small standing crop biomass compared to production turnover time= (standing crop biomass mg/m2)/(production mg/m2/day) green world hypothesis : terrestrial herbivores consumer relatively little plant biomass b/c they are held in check by a variety of factors, including predators, parasites, and disease o several factors that keep herbivores in check: plants have defenses against them nutrients, not energy supply, usually limit herbivores 54.4 Abiotic factors limit herb. Intraspecific competition can limit herb. #s Interspecific interactions keep herb. densities in check Biological and geochemical processes move nutrients btwn organic and inorganic parts of the ecosystem Because nutrient circuits involve both biotic and abiotic components, they are called biogeochemical cycles Biology 1510 Module #2 Part 4 Page 9 of 9 Water cycle: o Importance: water essential to all organisms; availability influences rates of ecosystem processes, particularly primary production and decomposition in terrestrial ecosystems Carbon cycle: o Importance: C forms framework for all organic molecules o Reservoirs: fossil fuels, sediments of aquatic ecosystems Nitrogen cycle: o Importance: N component of amino acids, proteins and nucleic acids; often limiting resource for plants o Reservoirs: mainatmosphere; otherssoil, sediment also fixated by lightning Phosphorous Cycle: o Importance: organisms require P as a major constituent of nucleic acids, o o Key processes: N2 converted into nitrogenous organic compounds by bacteria; o phospholipids, and ATP and other energystoring molecules Reservoirs: sedimentary rocks of marine origin, also soil, ocean(dissolved form) Key processes: weathering of rockssoil; taken up by consumers and distributed The Hubbard Brook Experimental Forest: This study demonstrated that the amount of nutrients leaving an intact forest ecosystem is controlled mainly by the plants. These effects of removing the trees are almost immediate, occurring within a few months, and continue as long as living plants are absent. 54.5 Human wear on environment...boring crap...acid rain, critical load of nitrogen, rising carbon dioxide lvlsglobal warming, ozone depletion...blah, blah, blah
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%% % Reference: Smith text, Section 2 and 3%% This homework is due Thursday, August 20th at midnight with a 6 hour grace% period. Submit your assignment as instructed in class. If the system% is not operational by the
Georgia Tech - CS - CS 1371
%=%% This homework is due on Thursday, August 28, 2008 at 11:45:00 PM with a% 6 hour grace period until Friday, January 19 at 6:00:00 AM. No late% submissions will be accepted. When you are finished, submit your% assignment to T-Square: (https
Georgia Tech - CS - CS 1371
%=% PROBLEM 1. Creating Vectors%-% % For the following exercises, do not use the direct entry method to% construct the vectors.%clearclc% (a) Construct a vector containing all of the even numbers between 6 and% 33, inclusive of the end
Georgia Tech - CS - CS 1371
clearclc%=% PROBLEM 2. Indexing Vectors%-%% You are given a vector &quot;vec&quot;, defined as:vec = [45 8 2 6 98 55 45 -48 75];mask = [true false false false false true true false true]; vec = vec(mask)% In a brief moment of insanity you decide tha
Georgia Tech - CS - CS 1371
clearclc%=% PROBLEM 3. Functions to use with Vectors%-%% You are given a vector &quot;vec&quot;, defined as:vec = [45 8 2 6 98 55 45 -48 75];% (a) Create a variable called &quot;vLength&quot; that holds the length of the% vector &quot;vec&quot; modified in Problem
Georgia Tech - CS - CS 1371
clearclc%=% PROBLEM 4. Linspace Applicatioin%-% % Write a Matlab script to plot sin(x) vs. cos(x). In creating your plot% you should vary x from -pi to pi. A similar vector (&quot;theta&quot;) to x was% created in Problem 1(d) above. You should fin
Georgia Tech - CS - CS 1371
clearclcload twovec.matredvec = [];x = 1;y = 1;test = false;while test = false &amp; x &lt;= length(onevec) if sum(redvec) &gt; 10 test = true; end if test = false redvec(y) = onevec(x); end if sum(redvec) &gt; 10
Georgia Tech - CS - CS 1371
clearclcload bigvec.matx = 1;test = false;while test = false if bigvec(x) &gt; 401 if rem(bigvec(x),2) = 0 if rem(x,2) = 1 test = true; num = bigvec(x) end end end
Georgia Tech - CS - CS 1371
clearclcload houses.mattheMax = 0;x = 1;y = 1;while x &lt;= length(prices) if crime_rate(x) &lt; .5 &amp; sizes(x) &gt; 1000 &amp; prices(x) &lt; 250000 quality = (sizes(x)/(prices(x)*crime_rate(x); if quality &gt; theMax theMax = qu
Georgia Tech - CS - CS 1371
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Georgia Tech - CS - CS 1371
function [A B C D E] = ABCs_cell_arrays(C, ca1, ca2)% PROBLEM 3. The ABCs of Cell Arrays%% This is a multi-part problem. Do each of the parts below.%% DO NOT CHANGE THE FUNCTION HEADER (the first line of code)% a) Creating. Create a cell ar
Georgia Tech - CS - CS 1371
function [A B C D] = ABCs_conditionals(x, y, z)% PROBLEM 4. The ABCs of Conditionals%% This is a multi-part problem. Do each of the parts below.%% DO NOT CHANGE THE FUNCTION HEADER (the first line of code)% a) if statements. x is a number.
Georgia Tech - CS - CS 1371
function [A A_method B B_method C] = ABCs_iteration(x)% PROBLEM 5. The ABCs of Iteration%% This is a multi-part problem. Do each of the parts below.%% DO NOT CHANGE THE FUNCTION HEADER (the first line of code)% 1) for loops. Below are two fo
Georgia Tech - CS - CS 1371
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Georgia Tech - CS - CS 1371
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Georgia Tech - CS - CS 1371
%PROBLEM 6%function output = cellUnwrap(A)while iscell(A{1}) = true A = A{1};endoutput = Aend
Georgia Tech - CS - CS 1371
function result = myStrCmpI(x, y) if (length(x) ~= length(y) result = false; return; enddiff = 'a' - 'A';i=1; while (i &lt;= length(x) &amp; (x(i) = y(i) | . (isletter(x(i) &amp; isletter(y(i) &amp; abs(x(i) - y(i) = diff)
Georgia Tech - CS - CS 1371
%PROBLEM 4%%% Write a function named myStrFindI that takes in two strings. Your% function should return a vector containing the starting index of all% the occurences of the first string within the second string. Your% function should
Georgia Tech - CS - CS 1371
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Georgia Tech - CS - CS 1371
%PROBLEM 2%function output = removeSpaces(A)% takes in a string and outputs the same string but with all the space characters removedindex = 1;while index &lt;= length(A); if uint8(A(index) = 32; A(index) = []; end index = index
Georgia Tech - CS - CS 1371
%PROBLEM 5%% Write a function named slowSort that takes in a vector, sorts it in % ascending order (smallest to largest), and then outputs it.%% Note: you may *not* use the built-in sort function in MATLAB.% function output = slowSort(A)
Georgia Tech - CS - CS 1371
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function [A B C D E F G H I J] = ABCs_structures(a_name, a_price, b_name, b_price, st1, st2, f1, var1)% PROBLEM 1. The ABCs of Structures%% This is a multi-part problem. Do each of the parts below.%% DO NOT CHANGE THE FUNCTION HEADER (the firs
Georgia Tech - CS - CS 1371
%=% Problem 3. Sorting Structures%-%% In homework 4, you implemented an algorithm to sort a vector.% You will now implement the same algorithm to sort a structure array based% on one of its fields. To do this, please complete parts A and B bel
Georgia Tech - CS - CS 1371
% Problem Statment:%% Write a function named structFromCell that takes in a cell array and% returns a structure constructed from the cell array. The elements in% the odd indexes of the cell array should determine the field name and% the
Georgia Tech - CS - CS 1371
%=% Problem 2. Searching through a structure array%-%% Problem Statment:%% Write a function named structSearch that takes in a structure array, a% fieldname, and a value. The function should return a new structure% array containing ever
Georgia Tech - CS - CS 1371
function S = structSort2(A,str)a = A;b = A;[r c] = size(A);vec = [];if r = 1 a = A; [v loc] = minStruct(a,str); vec = [vec v]; a(loc) = [];else for x = 1:r for y = 1:c [v loc] = minStruct(b,str);
Georgia Tech - CS - CS 1371
%=% Problem 3, part B. Sorting the structure array%-%% Problem Statment:%% Write a function named structSort that takes in a structure array and a% string. The string specifies the name of a field in the structure% array that will only
Georgia Tech - CS - CS 1371
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Georgia Tech - CS - CS 1371
function genStats(excel)[num str cell]= xlsread(excel);[row col]=size(cell);avg=mean(num,2);for x=2:row cell{x,col+1}=avg(x-1);endtotavg=mean(num);for y=2:col cell{row+1,y}=totavg(y-1);endcell{end,end}=mean(totavg);cell{1,end}='Aver
Georgia Tech - CS - CS 1371
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Georgia Tech - CS - CS 1371
%Write a function called myCSVwrite which takes in a cell array of doubles%and chars and a filename, returns nothing but writes a file with each of the cells'%contents seperated by commas. The cell array may be two dimensional, you%should put eac
Georgia Tech - CS - CS 1371
% Write a function called snake that takes in an array and a number% indicating how many places to &quot;snake&quot; the array as described below.% Snaking the vector involves shifting the numbers down columns, and % appending the overflow onto the top of
Georgia Tech - CS - CS 1371
function numwords=wordCount(string)fh=fopen(string,'r');words=';count=1;while ischar(words); words=fgets(fh); [tk rest]= strtok(words); while ~isempty(rest) [tk rest]= strtok(rest); count=count+1; endend numwo
Georgia Tech - CS - CS 1371
%=% Problem 5. Plotting Simple Shapes%-%% Problem Statement:%% Write a function called plotPolygon that will take in two vectors of the same% length and have no outputs. The first vector will contain the x values for the% polygon and t
Georgia Tech - CS - CS 1371
%=% Problem 7. Plotting Pretty Colors%-%% Problem Statment:%% Write a function named plotRainbow that takes in the radius, and an% increment value. Starting at the initial radius, plot 6 semicircles to% create a rainbow. The order of
Georgia Tech - CS - CS 1371
%=% Problem 1. Signal Processing%-% After graduating from Georgia Tech with a 4.0 GPA, you easily get a job% with SETI (search for extra terrestrial intelligence)% as an extra-terrestrial signal analyst. One day, while you are% working on the
Georgia Tech - CS - CS 1371
%=% Problem 2. Finding the determinant of a matrix using recursion%-% % Problem Statement:%% Write a function called recurDet which takes in a square matrix and % returns the determinant of that matrix using recursion.%% Hint: Use
Georgia Tech - CS - CS 1371
%=% Problem 4. Recursive Math%-%% Problem Statement%% Write a function named recMod that takes in 2 numbers and% returns the remainder of the first number divided by the second number.% This function should use recursion to produce th
Georgia Tech - CS - CS 1371
%=% Problem 1. Finding the sum of a vector with recursion%-%% Problem Statement:%% Write a function called recurSum which takes in a vector and returns% the sum of that vector using recursion.% % Notes: % -You *must* use rec
Georgia Tech - CS - CS 1371
%=% Problem 6. Plotting a Slinky%-%% Problem Statment:%% Write a function named slinky which takes in a number r, which is the % number of revolutions, and a number n, which is the number of points.% Your function should then plot a 3D
Georgia Tech - CS - CS 1371
%=% Problem 3. Arrays and Recursion%-%% Problem Statment:%% Write a recursive function named sumRings that consumes an M by N array% and returns a vector of the sums of its rings of elements. Consider:% [1 1 1 1 1 1 1% 1 2
Georgia Tech - CS - CS 1371
%=% Problem 8. Designing a Tunnel.%-%% Create a recursive function, tunnel.m, that will take in three inputs: a% radius (r), and two scalars, x and y. Plot a circle using the% coordinates (x,y) as the center and the radius (r) as your radius. C
Agnes Scott College - MGMT - 303
Besanko &amp; Braeutigam Microeconomics, 3rd editionSolutions ManualChapter 2 Supply and Demand AnalysisSolutions to Review Questions1. Excess demand occurs when price falls below the equilibrium price. In this situation, consumers are demanding a
Agnes Scott College - MGMT - 303
Agnes Scott College - MGMT - 303
Agnes Scott College - MGMT - 303
1. 2. 3.4. 5.6.7.8.9.Ch. V What is the cost-minimizing level of output? a. Given a desired level of o/p, isoquants and isocosts provide information to determine o/p level. Cost min level of inputs/ a. Determined by point at which ratio of
Agnes Scott College - MGMT - 303
ACCT 245 BronsteinExercise 3-13b a. Contribution margin per unit = $25 - $7 = $19 Break-even point in units = $81,000 19 = 4500 Break-even point in dollars = $25 x 4500 = $ 112500 (Fixed cost + Desired profit) Contribution margin per unit = ($81,