This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*This
** preview**
has intentionally

**sections.**

*blurred***to view the full version.**

*Sign up*
**Unformatted text preview: **MAC1105 024 027 Name: K 5 ﬂ Project2 (circle your section) due October 25, 2011 Please follow all directions carefully. Include as much relevant work as possible to ensure maximum
credit. Where explanations are requested please write legibly and use complete sentences. {20 pts) 1 . QUADRATIC FUNCTIONS: A baseball is hit and follows a parabolic are due to gravity. Let t represent the number of seconds the ball is in the air, let 1: represent the horizontal distance in feet the ball travels, and let y represent the vertical
height the ball attains, also measured in feet. The following functions can both be used to model the path of this ball. f(t) = —16tZ + 64.3t + 3 (height as a function oftime)
g(x) = — 0.002751:2 + 0.84:; + 3 (height as a function of distance) a) Use your calculator to accurately graph the relevant portion of both functions over the following grids. Label all intercepts and
maximum points, and state the domain and range of each function. You may round inexact answers to the nearest whole number. 136 281} 300 (3's)°) Domain: 0&- 'L ELI Domain: 0!; X‘ ils
Range: 05 “£63 Range: 05 “562 b) For how many total seconds is the ball in the air?
her haul-.1. {win-ref“ o-F grepk a». le-Flr . - aims! -
c) How many feet does the ball travel until it lands? hormonal-J. t'wluupt. .4” grapkw. r15”. c) 3153. d) What is the maximhm height the ball attains?
. d) 6 9 ﬂ.
intakes-l k- VLLN... C sm val“. Car bo-lk. graphs) : _. e) If there is a 10 foot tall wall at a distance of 300 feet from the batter, will the ball clear the wall? Show how you decide and circle the correct choice.
@ or no 900% ‘1 ¢+ , so am a. loan all. want
300 Q- .l‘l' will ClQM '“M- wall. (300)?» 300
f) If the ball clears the wall, by how many (vertical) feet will it this happen? If the ball does not clear the wall, skip this part. '35“ " [Oi-1L = 9.3%. sift-— (14 pts) 2. POLYNOMIAL FUNCTIONS: The following table lists the amount N of natural gas consumption in year t,
measured in quadrillion B'IU’s, with t = 0 representing the year 1970. 3) Enter the data in L1 and L; of your calculator and ﬁnd a third degree polynomial to model this data. E
Write coefﬁcients wiﬂi enough decimal-places to ensure reasonable accuracy. 3) Na): 0.0015 “.15 6-003 IQS‘l'Ea-tlﬁié'ﬂét + I? .5535“)! b) Graph your function as well as the data on the grid below. c) Use the formula to estimate N (one decimal place) in years N 1995 (interpolation) and 2015 (extrapolation). Label these
points on your graph.
WW Mas) a: MG 1995; m
(users)
35 3015: ”('45) g 32.5 2015:3113 «Year l-iI d) Use the formula to estimate the year that N was
approximately 25 quadrillion BTU’s. (Hint: Use your 29 35 33 40 M5 50 calculator to ﬁnd where a horizontal line at N = 25 intersects
[Q10 I‘l‘ls - 30 I 5 the graph. Use this point to answer the question1 round the year
to the nearest whole number.
m yea-rs to" the = Don <0ﬂL. (20 pts) 3. RATIONAL FUNCTIONS: The number of fulltime faculty at a college has been increasing steadily since the
college was founded in 1970, and consequently so has the number of parking spaces reserved for faculty. If we let t measure the number of years since 1970, the formula F02] = 60 + 11“ gives the number of fulltime faculty members in year t and the
Pt‘) formula Pﬂ) = 90+ 9t gives the number of parking spaces reserved for the faculty. Deﬁne R(t) = FE?) W ‘
'H 'cQCwuy "lamb“; 1 “AL miao__ 0c reserved. poi-kin.) gates per Real-Ir member. a) Explain what RU) measures. R (It) “NI-USING: 5 b. F and P are both linear. Interpret the slope and y-intercept of both functions in the context of this problem. - The slopeofFis 10 and represenrsiacnllqr—hnsnncmLaLuakﬂmr yew.
1: The vertical interceptofthe graph ofFis 60 andrepresents wt. [tho iggt 1; mg eoﬁgglgy member! - TheslopeofPis :I andrepresentsmm W mcm& 4:" t (All. 0'? ‘1 Per Yr; 0 Theverticalinterceptofthegraphof?is 90 andrepresents JUL H70 ‘HKOLL. wet; ‘lO Pﬂfkl‘lg
Spaces Wanna-(Q .Cor Fatally membus. c) Evaluate R(0) and interpret this answer in the context of this situation. . c L5 ' .
“03:329.. M92... 8.9.45 )m FLO) ' 604.100!) 60 ’ . . _
In mo (i=0) 444w; Mia. L5 who, seduces MSeer
300 Main. Cu,“ Hm Rad-i7 Member. d) Evaluate R150) with two decimal place accuracy and interpret this answer in the context of this situation. [2(50): Egg-1. M 1-. 25.696 454qu d) 0q6 - F (50) 60 {(10050)
in ‘10 ac U150) 41mm. will lea. appwxima‘leill O-QQ, pwkxins spaces
"Sew—€69. For earl.» Cull ‘i'L‘ML (“any MMIMP. e) Sketch the graph of R for t 2 0 . Use a dashed line to indicate the horizontal asymptote of this graph, and label this asymptote
with its equation. Label the points that correspond to your previous two answers. - _ QO+Q+
9(0- eonoe' as .-L awe , lid. {mi-Hal valus 030 0-9 ‘10 “Leo beam Less
. mull less s'lgn‘nﬁcoui' dual H " "am. {who RC-Dgeis chm-
emit clour- "m 4U. mi-u‘o 0‘
'va slopes . ' ch _
Rag-s H — 0.5! "EB EB 31} 4!? SE SE E El} ﬂ Solve the equation R(t) = 1, either algebraically or using your calculator and label this point on your graph Interpret this answer in context 22:2: =1 e; Qo+q+=ee+10t -' 9‘? n J«=30 '_
"6° _'°° ‘ 30 years oil» [4 7a is +1.4
3’0 if: ' ‘ 2': Year 3000. 'Tkail' ms. 4M. 7804- M Mwu mac-Hy
_ On... er"“'5 some. [€59le
For QdeL. gull Mm (1‘:tu Member. 10 =7.-l: (20 pts) 4. POWER FUNCTIONS/VARIATION: Consider a 3 dimensional object (it could be a twig or a log or a squirrel or
an elephant or whatever, it doesn‘t matter). Suppose x is a linear measure of this object. (it could represent height, width, or whatever. Again, it doesn’t matter.) Let A(x) = 6x2 measure the total surface area of this object, and V(x) = 213 be a
measure of the volume.
X -) 3x a) By what factors do the Surface area and volume increase if x triples in size?
Pl (.3K)‘: 6(3X5": 6'51 x3 9 ‘1. 6K; 3: q , HCKB Surfacearea: 4‘ ﬁg? Sbm. Cr
v (3m 30*)”- a-lamc’: may? ewes Balk. P. Motv a... swan}: E: :E I: Q +9 K VolumeL—llmr b) Fill in the table below and draw graphs for both ﬁtnctions
on the same graph. Clearly indicate which 15 which. 1; (inches) A(x) (sq. inches) V(X) (cubic inches) 0 1 2 3 : as we
6 air» H33 c) Derive and simplify a formula for the surface area to volume ratio [ROG = A00] of this object.
Pl (____:_<_) O K a “s W) 3‘
RCX )— —""""_3""‘ :- -—- OK 3x"! R(X) =_.__.x__.__
v (10’9M X
c) Fill In the table. d) Draw a graph of R. e) What happens to the value of R as X —) +00. 9
V): - I I I I I I I I as X 3845 blasef' M6!- \Nsﬁex) Ho‘-
iRo Value 09 R gels closer dwell clan-r
6 vioO(bwl:er-aeisib0)
3 0 How 18 your answer to e) indicated on the graph?
0'6 PM 3a kits; 0. lama-who-
{'3 Pan‘wtptolt aci'i'LlL Y'dlﬂis 0L5 223456?8916 X-}+GO. g) Use the individual graphs of A(x) and V(x) to explain the shape of the graph of 11(1) . Your explanation should involve the
rate at which the surface area of this object grows compared to the rate at which the volume grows. Frm ~an. amp“ M P‘s/(1' D In", cm He. M 4L1. volume LLi‘i'iMH"
65W: chtsi-er “my. ‘HNL Sureﬁre me. ﬁrms The”. 4L1. who r91 4h. 44400 keeps gelling) smug! 4.5 4L9, obloc-i' 5””5 lager.
R is inwvselu 2w mggriimaki‘v K. (16 pts) 5. COMPOSITION OF FUNCTION S: A car accelerates at a constant rate of 6 feet per second per second. The
2 S
formula S(t) = 6t computes the speed of the car in feet per second aﬁer t seconds, and the formula D(S)— — E computes the total distance traveled in feet when this car has reached a speed of S feet per second. a) Given choices 1) speed, 2) distance and 3) time. Place the appropriate word inside each circle, and place appropriate units
below each circle. pawl: 21) m. w [email protected]
pow} l0—-—) (60) qpmg...’ (use units:_'g’1m_ mush b) Use the speed function to compute the speed of this car after 10 seconds. Include appropriate units. SC—D' 64: % sClo) =(oo (fa-k p3,- M wiggles. c) Use your previous answer and the distance function to aeompute the distance traveled In 10 seconds Include appropriate units. D©=ng e o(eo)=—5_-— L- "500 m. s% d) Derive and simplify the composite formula (D0 S)(t) . a
(‘D as) (L) = b [$05] = I) (61) = L? =- 31L“ 3;, amy- e) Use your formula from part i) (show work) to evaluate (D 0 8X10). Include appropriate units. (Dos) (4:) = 3+." $ (Dos)(lo)= 3C1o)3= 300 R. [10 pts) 6. IN VERSE FUNCTIONS: T = Hm) = 182 — 3111 represents the temperature T in degrees Fahrenheit of a water sample after to minutes of coolmg. @
owns a) If the cooling began at noon, what was the water temperature at 12:30 pm? MM!» . O .—
M 3:33;“) T: ﬂso)» lea—5(a) = Cl; )Jl”i-—-— b) Derive a formula for m = f ‘1 (T) by solving the original formula for m. ‘ _ l%§.*T
T— 123-3“ :5 311M lﬁ'a-‘T 1““ b)m=f“(T)=._3-
.. l‘3Q'r
m.-
3 c) The freezing point of water is 32°F. Use your inverse formula from part b (show work) to determine the time of day this
sample of water will freeze. _, 1833- 32 ._ lee -
15;, l (-53): - ~3— = ‘50 mmwl-u D
«:40? “0% $4 , _ Mind‘s demos ...

View
Full Document