In the Budget Challenge, you had an opportunity to increase or decrease taxes. What changes did you select? Who is helped or harmed by the changes that you proposed? How did the overall debt change as a result of your proposed changes?

What does the slope represent?

Consider the following statements regarding how government spending responds to changes in aggregate income, wealth, and interest rates.

A. Government spending responds directly to changes in aggregate income, wealth, and interest rates. Changes in aggregate income, wealth, and interest rates automatically cause government spending to change.

B. Government spending does not respond directly or indirectly to changes in aggregate income, wealth, or interest rates. Changes in aggregate income, wealth, and interest rates do not have any effect on government spending.

C. Government spending responds indirectly to changes in aggregate income, wealth, or interest rates. During a recession, aggregate income and wealth will fall and the government may decide to increase government spending to stimulate output and jobs in the economy.

Which of the statements are true?

Statement C

Statement A

Statement B

The following data represent the amount of money and invenstor has in an investment account each year for 10 years.

a. Let x=number of years since 1994 and find an exponential regression model of the form y=ab* for this data set, where y is the amount in the account x years since 1994.

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b. If the investor plans on retiring in 2021, what will be the predicted value of this accoutn at that time?

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c. When will the account be worth $50,000?

d. Make a graph of the scatterplot and exponential model below.

Year value of account

1994 $10,000

1995 $10,573

1996 $ 11,260

1997 $11,733

1998 $12,424

1999 $13,269

2000 $13,698

2001 $14,823

2002 $15,297

2003 $16,539

The values of certain types of collectibles can often fluctuate greatly over time. Suppose that the value of a particular limited edition figurine is found to be able to be modeled by the function

?(?) = −0.01?⁴ + 0.47?³ − 7.96?² + 49.18? + 65 for 0 ≤ ? ≤ 20 where ?(?) is in dollars, t is the number of years after the figurine was released, and ? = 0 corresponds to the year 1999.

a) What was the value of the figurine in the year 2009?

b) What was the value of the figurine in the year 2019?

c) What was the instantaneous rate of change of the value of the figurine in the year 2002?

d) What was the instantaneous rate of change of the value of the figurine in the year 2019?

e) Use your answers from parts a-d to estimate the value of the figurine in 2020.

10.30  Grade inflation. The average undergraduate GPA for American colleges and universities was estimated based on a sample of institutions that published this information.¹³ Here are the data for public schools in that report:

Do the following by hand or with a calculator and verify your results with a software package.

1. (a) Make a scatterplot that shows the increase in GPA over time. Does a linear increase appear reasonable?

2. (b) Find the equation of the least-squares regression line for predicting GPA from year. Add this line to your scatterplot.

3. (c) Compute a 95% confidence interval for the slope and summarize what this interval tells you about the increase in GPA over time.