MATH 176

UNIT 1 HOMEWORK ASSIGNMENTS

General Instructions

  • The answers to all problems are in the back of the book, beginning on page A-1. It is important to check your homework.
  • Homework problems are listed by Topic, not day and you are responsible for the homework for all topics covered in each class period.
  • Part C are supplemental problems based on class work and may not be covered in the book. Answers to these problems are at the end of the assignments for this unit.

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UNIT 0 – Function Review

Topic 1: Linear and Absolute Value Functions

A)Text: Read pages 1 – 8, 10 – 25.

B)Exercises Topic 1, pages 25 – 29: 15–19 odd, 61, 63(part c, use window [0,40] for x and [20,35] for y), 65–77 odd.

C)Additional Exercises

i)Exercises Topic 1, page 27: Use the following directions to do 49 – 54 all

a)Match each equation to a graph

b)State the domain and range for each function

ii)Linear Depreciation (use formula on page 18 in the book).

A company constructs a warehouse for $1,725,000. The warehouse has an estimated useful life of 25 years, after which its value is expected to be $100,000. Write a linear function giving the value of the warehouse during its 25 years of useful life.

Topic 2: Non-Linear Functions.

A)Text: Read pages 30 – 48.

B)Exercises Topic 2, pages 48 – 50: 1–12 all, 51–61 odd, 69

C)Additional Exercises

i)Let , Find

ii)The increase in cell phone use in pre-teens can be modeled with the power regression model . Use the model to approximate in what year there will be 40 million users.

Topic 3: Rational and Piecewise Defined Functions

A)Text: Read pages 53 – 71

B)Exercises Topic 3, pages 71 – 75: 17–23 odd, 27, 31, 45, 53.

Topic 4: Regression and Modeling

A)Text: Read pages 76 – 87

B)Exercises Topic 4 pages 87 – 91: 9, 11, 15, 19, 21

C)Additional Exercises

i)The net earnings of Gap Inc. from 1997 through 2006 is shown on the table below.

Year / Net earnings
(millions of dollars)
1997 / 211
1998 / 258
1999 / 320
2000 / 354
2001 / 453
2002 / 534
2003 / 825
2004 / 1127
2005 / 877
2006 / –8

a)Observe a scatter plot of the data in the table and explain why a piecewise model is needed to describe the data set.

b)Divide the data into two subsets. Use a quadratic and linear regression to create a piecewise linear model to fit this data. Be sure to fully define your model.

c)Use your model to predict net earnings in 2010.

UNIT 1 Limits and Derivative

Read pages 97 – 100 of the text as an overview

Topic 5  Introduction to Limits

Day 1

A)Text: Read pages 101 – 115, 120 – 122

B)Exercises Topic 5, pages 131 – 135: 1–31 odd, 35, 37, 41(factor first).

C)Additional Exercises

i)Using a graphing calculator or converge to determine the limits for problems 39, 43, 45, and 47 on page 134.

Day 2

A)Text: Read pages 115 – 120, 122 – 127

B)Exercises Topic 5, pages 131 – 137: 51, 53, 55, 57, 59, 69–87 odd, 93

Topic 6: Continuity

A)Text: Read pages 138 – 148

B)Exercises Topic 6, pages 148 – 150: 1–39 odd, 49, 51, 53.

Topic 7: Rates of Change and Slope

A)Text: Read pages 153 – 167 (before example 10)

B)Exercises Topic 7, pages 173 – 177: 1–7 odd, 23, 25, 37, 41

C)If a quantity changes from a value of m to a value of n over a certain interval, then the percentage change is the change divided by the first value and then multiplied by 100.

i)Using the data from problem 3 on page 174, find the percentage change in income

a)Between 1930 and 1940

b)Between 1950 and 1970

c)Between 1990 and 2004

ii)Using the date from problem 5 on page 174, find the percentage change in average cost of a new home.

a)Between 1930 and 1940

b)Between 1950 and 1970

c)Between 1980 and 1990.

Topic 8: Introduction to the Derivative

A)Text: Read pages 179 – 182(through example 5), 185 – 187

B)Exercises Topic 8, pages 189: 1–9 odd, 27, 29, 37, 39abc

Topic 9: Derivatives of Algebraic Functions

A.Text: Read pages 192 – 204

B. Exercises Topic 9, pages 204 – 207: 1–25 odd, 35, 41, 43, 47, 51, 53, 55, 57, 59

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Topic 1 Part C:

i)

49. Graph C

50. Graph E

51. Graph A

52. Graph E

53. Graph B

54. Graph D

ii) where t is number of the years.

Topic 2 Part C:

i)

ii) In year 2018, approximately 14.8 years since 2004, there will be 40 million pre-teen cell phone users.

Topic 4 Part C:

i) Scatter plot of all data points, where x is years since 1990. Divide data in years 1997-2004, 2004-2007.

Using the linear model to predict earnings in 2010, x=20, Earnings will be -2172 million. It is unlikely that this model is sustainable for the business.

Topic 5 Day 1 Part C:

39. Limit does not exist

43. 1/2

45. Limit does not exist

47. Limit does not exist

Topic 7 Part C:

i)Using the data from problem 3 on page 174, find the percentage change in income

a)Between 1930 and 1940:

b)Between 1950 and 1970:

c)Between 1990 and 2004:

ii)Using the date from problem 5 on page 174, find the percentage change in average cost of a new home.

a)Between 1930 and 1940:

b)Between 1950 and 1970:

c)Between 1980 and 1990:

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