# Register now to access 7 million high quality study materials (What's Course Hero?) Course Hero is the premier provider of high quality online educational resources. With millions of study documents, online tutors, digital flashcards and free courseware, Course Hero is helping students learn more efficiently and effectively. Whether you're interested in exploring new subjects or mastering key topics for your next exam, Course Hero has the tools you need to achieve your goals.

1 Page

### c674

Course: MATH 160, Fall 2008
School: Boise State
Rating:

Word Count: 400

#### Document Preview

PRESENT 9. VALUE OF AN INVESTMENT Suppose an invest- ment is expected to generate income at the rate of R(t) = 200,000 dollars/year for the next 5 yr. Find the present value of this investment if the prevailing interest rate is 8%/year com- pounded continuously. 10. FRANCHISES Camille purchased a l5-yr franchise for a computer outlet store that is expected to generate income at the rate of R(t) = 400,000...

Register Now

#### Unformatted Document Excerpt

Coursehero >> Idaho >> Boise State >> MATH 160

Course Hero has millions of student submitted documents similar to the one
below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.

Course Hero has millions of student submitted documents similar to the one below including study guides, practice problems, reference materials, practice exams, textbook help and tutor support.
PRESENT 9. VALUE OF AN INVESTMENT Suppose an invest- ment is expected to generate income at the rate of R(t) = 200,000 dollars/year for the next 5 yr. Find the present value of this investment if the prevailing interest rate is 8%/year com- pounded continuously. 10. FRANCHISES Camille purchased a l5-yr franchise for a computer outlet store that is expected to generate income at the rate of R(t) = 400,000 dollars/year. If the prevailing interest rate is 10%/year compounded continuously,. find the present value of the franchise. , 11. THE AMOUNT OF AN ANNUITY Find the amount of an annuity if \$250/month is paid into it for a period of 20 yr, earning interest at the rate of 8%/year compounded con- tinuously. 12. THE AMOUNT OF AN ANNUITY Find the amount of an annuity if \$400/month is paid int6 it for a period of 20 yr, .. earning interest at the rate of 8%/year compounded con- tinuously. 13. THE AMOUNT OF AN ANNUITY Aiso deposits \$150/month in a savings account paying 8%/year com- pounded continuously. Estimate the amount that will be in his account after 15 yr. 14. CUSTODIAL ACCOUNTS The Armstrongs wish to estab- lish a custodial account to finance their children's education. If they deposit \$200 monthly for 10 yr in a savings account paying compounded 9%/year continuously, how much will their savings account be worth at the end of this period? 15. IRA ACCOUNTS Refer to Example 4, page 475. Suppose Marcus makes his IRA payment on April 1, 1990, and annu- ally thereafter. If interest is paid at ,the same initial rate, approximately how much will Marcus have in his account at the beginning of the year 2006? 16. PRESENT VALUE OF AN ANNUITY Estimate the present value of an annuity if payments are \$800 monthly for 12 yr and the account earns interest at the rate of 10%/year com- pounded continuously. 17. PRESENT VALUE OF AN ANNUITY Estimate the present value of an annuity if payments are \$1200 monthly for 15 yr and th~account earns interest at the rate of 10%/year com- pounded continuously. 18. LOTTERY PAYMENTS A state lottery commission pays the winner of the "Million Dollar" lottery 20 annual installments of \$50,000 each. If the prevailing interest rate is 8%/year compounded continuously, find the present value of the win- ning ticket. 19. REVERSE ANNUITY MORTGAGES Sinclair wishes to sup- plement his retirement income by \$300/month for the next 10 yr. He plans to obtain a reverse annuity mortgage (RAM) on his home to meet this need. E~timate the amount of the
Find millions of documents on Course Hero - Study Guides, Lecture Notes, Reference Materials, Practice Exams and more. Course Hero has millions of course specific materials providing students with the best way to expand their education.

Below is a small sample set of documents:

Boise State - MATH - 160
mortgage he will require if the prevailing interest rate is12%/year compounded continuously.20. REVERSE ANNUITY MORTGAGE Refer to Exercise 19.Leah wishes to supplement her retirement income by\$400/month for the next 15 yr by obtaining a RAM. Esti
Boise State - MATH - 160
a. Compute the coefficient of inequality for each Lorentzcurve.b. Which profession has a more equitable income distribution?23. LORENTZ CURVES A certain country's income distributionis described by the function14 1f(x) = -,- X2 + - x15 15a. S
Boise State - MATH - 160
Problems for Section 8.41. Draw a graph, with time in years on the horizontal axis, of what an income stream might looklike for a company that sells sunscreen in the Northeast.2. A company that owes your company money offers to begin repaying the
Boise State - MATH - 160
-. - ~- ~- -7. (a) If you deposit money continuously at a constant rate of \$1000 per year into a bankaccount that earns 5% interest, how many years will it take for the balance to reach\$10,000?(b) How many years would it take if the account had \$
Boise State - MATH - 160
Problems for Section 8.2.1. Imagine a hard-boiled egg lying on its side cut into thin slices. First think about vertical slicesand then horizontal ones. What would these slices look like? Sketch them.2. Find the volume of a sphere of radius r by
Boise State - MATH - 160
8.2 APPLICAnONS TO GEOMETRY 43514. Rotate the bell-shaped curve y = e-xz/2 shown in Figure 8.21 around the y-axis, forming ahill-shaped solid of revolution. By slicing horizontally, find the volume of this hill.y1Y = e-xzJ2xFigure 8.2115. The
Boise State - MATH - 160
21. Figure 8.22 is a graph of the function1(X-X)Y~2e +e .It is called a catenary and represents the shape in which a cable hangs. Find the length of thiscatenary between x = -1 and x = 1.y 1Y = -(eX +e-X)2x1Figure 8.22.22. , Compute the p
Boise State - MATH - 160
Problems for Section 8.3I. A water tank is in the fonn of a right circular cylinder with height 20 ft and radius 6 ft. If tIJtank is half full of water, find the work required to pump all of it over the top rim. (NoteI cubic foot of water weighs 6
Boise State - MATH - 160
9. Show that the escape velocity needed by an object to escape the gravitational influence of aspherical planetof density p and radius R is proportional to R and to ~.10. Calculate the escape velocity of an object from the moon. The acceleration du
Boise State - MATH - 160
ems for Section 8.6..1. Consider the fishing data given in Example 1 on page 463. Show that the area under thedensity function in Figure 8.44 is 1. Why is this to be expected?2. Find the mean daily catch for the fishing data in Figure 8.44, page
Boise State - MATH - 160
(b) What was the median income?(c) Sketch a density function for this distribution. Where, approximately, does your densityfunction have a maximum? What is the significance of this point, in terms of incomedistribution? How can you recognize this
Boise State - MATH - 160
REVIEW PROBLEMS FOR CHAPTER EIGHT1. (a) Sketch the solid obtained by rotating the region bounded by y = yf&quot;i, x = 1, and y = 0around the line y = O. -(b) Approximate its volume by Riemann sums, showing the volume represented by eachterm in your s
Boise State - MATH - 160
Antiderivatives and Indefinite Integrals Worksheet Evaluate the following indefinite integrals 1.-2 dx =2.2x 5dx =3.3t - 7dt =34.2u 4 du =5.3x-2 3dx =6.1 dx = 3x 5 3 dt = t7.8.- ( 1+ u + u ) du =29.- ( 0.3t
Boise State - MATH - 160
Antiderivatives and Indefinite Integrals Worksheet Evaluate the following indefinite integrals 1.-2 dx =2.2x 5dx =3.3t - 7dt =34.2u 4 du =5.3x-2 3dx =6.1 dx = 3x 5 3 dt = t7.8.- ( 1+ u + u ) du =29.- ( 0.3t
Boise State - MATH - 160
Area Between Curves Worksheet1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.Key1. 2. 3. 4. 5. 6. 7. 8.
Boise State - MATH - 160
Definite Integrals Worksheet Evaluate the following definite integrals 1.)4 - 2( 3 x - 5)dx =2.) ( 2x - 10e x )dx =3.) (0 2 14x dx =)4.2 + x x 1 = dx 5.) ) )1 0( u ) ( u + 3 u ) du =1 dx = x6.8 47.
Boise State - MATH - 160
Definite Integrals Worksheet Key Evaluate the following definite integrals 1.)4 - 2( 3 x - 5)dx =4 2 3 3 3 48 12 x - 5 x = ( 4) 2 - 5 ( 4) ( - 2) 2 - 5 ( - 2) - 20 + 10 4 - 16 = - 12 - = - = 2 2 2 2 2 2 2.
Boise State - MATH - 160
Differential Equations Worksheet1.2.3.4.5.6.7.8.9.10.11.12.13.14.15.16.17.18.19.20.21.22.23.24.25.26.27.28.29.30.31.32.33.34.35.36.37.38.39.40.Key1. 2. 3. 4. 5. 6. 7.
Boise State - MATH - 160
Definite Integral Word ProblemsExample 1 An empty bucket is placed under a tap and filled with water. t minutes after the bucket has been placed under the tap. The rate of flow of water into the bucket is equal to 2.3 - 0.1t gallons per minute. How
Boise State - MATH - 160
Derivatives - Chain Rule Worksheet Key 1. f ( x ) = ( 1 - x )3f ' ( x ) = -3 ( 1 - x )22. f ( x ) = 2 ( x 3 - 1) 3. f ( x ) =5f ' ( x ) = 30 x 2 ( x 3 - 1)4-3 1 ( 2x 2 + x ) 23 ( 1+ 4x ) df =- dy 2 ( 2x 2 + x )1 d ( y ) = ( 3 ) ( 3
Boise State - MATH - 160
Derivatives - Chain Rule 1. f ( x ) = ( 1 - x )3f' ( x) =2. f ( x ) = 2 ( x 3 - 1)5f' ( x) =3. f ( x ) =-3 1 ( 2x 2 + x ) 2df = dy4. y = ( 3 x 2 - 2 x + 1) 23d ( y) = dx dy = dx45. y = 3 x 2 - x6. y = ( x - 1)2( 2 x + 1)
Boise State - MATH - 160
Derivative Problems Use the definition of derivative to solve the following. 1. f ( x ) = 3x + 5 f' ( x) =2. y = x 3dy = dx3. f ( x ) = x 3 - 4 x 2df = dx4. y =1 5xd ( y) = dx5. f ( x ) = - x 2 + 3xf' ( x) =Use the rules of differ
Boise State - MATH - 160
Derivative Worksheet Use the definition of derivative to solve the following. 1. f ( x ) = 3 x + 5 f' ( x) =2. y = x 3dy = dx3. f ( x ) = x 3 - 4 x 2df = dx4. y =1 5xd ( y) = dx5. f ( x ) = - x 2 + 3 xf' ( x) =Use the rules of dif
Boise State - MATH - 160
Continuityy = f ( x)1. What is the domain of f ' ( x ) ? 2. What is the range of f ' ( x ) ? 3. Find the x -intercept(s) of f ( x ) ? 4. Find the y -intercept(s) of f ( x ) ? 5. f ( -8 ) = _ f ( 2 ) = _ f ( -4 ) = _ f ( 8 ) = __6.x - 6-lim f
Boise State - MATH - 160
Continuity and DerivativesDefinition of continuous functionSecant becoming the tangent line
Boise State - MATH - 160
Derivatives - Product Rule Worksheet 1. f ( x ) = ( 2 x 2 - 1) ( x 3 + 3 ) f' ( x) =2. f ( x ) = ( x 3 - 12 x ) ( 3 x 2 + 2 x )f' ( x) =3. f ( x ) = 3 x 2 ( x - 1)df = dy4. y = ( 5 x 2 + 1) 2 x - 1()d ( y) = dx dy = dx5. y = ( x 3 -
Boise State - MATH - 160
Derivatives - Product Rule Worksheet Key 1. f ( x ) = ( 2 x 2 - 1) ( x 3 + 3 ) f ' ( x ) = 10 x 4 - 3 x 2 + 12 x2. f ( x ) = ( x 3 - 12 x ) ( 3 x 2 + 2 x )f ' ( x ) = 15 x 4 + 8 x 3 - 108 x 2 - 48 x3. f ( x ) = 3 x 2 ( x - 1)df = 9x 2 - 6x dy
Boise State - MATH - 160
Derivatives - Quotient Rule Worksheet 11. f ( x ) = 1 x -2 x -1 2x + 1 x 2x - 4 f' ( x) =12. f ( x ) =f' ( x) =13. f ( x ) =df = dy14. y =x2 + 1 x2 - 1d ( y) = dx15. y =x x +12dy = dxx2 + 2 16. y = 2 x + x +1 x2 + 1 xy' =17
Boise State - MATH - 160
Derivatives - Quotient Rule Worksheet Key 11. f ( x ) = 1 x -2 f' ( x) = -1( x - 2)3212. f ( x ) =x -1 2x + 1f' ( x) =( 2 x + 1)213. f ( x ) =x 2x - 4df -4 = dy ( 2 x - 4 ) 2 d -4 x ( y) = 2 2 dx ( x - 1)14. y =x2 + 1 x2 - 1
Boise State - MATH - 160
Simple Linear RegressionLeast Square Curve Fitting1PurposeAssume that two quantitative variables that are measured on the same items are sampled from a population. We get n pairs of observations: (x1, y1),.,(xn ,yn) Our aim is to develop a mode
Boise State - MATH - 160
Math 160 Calculus Problem 27, page 42 Regression ExampleFirst, we enter the 5 columns of data into lists, L1 - Year, L2 - Men's 100 Times, L3 - Women's 100 Times, L4 - Men's 200 Times, L5 - Women's 200 Times.For each set of times we need to: a) l