1. The following table shows the number P of design patents awarded by the U.S. Patent and Trademark Office from 1950 through 2010.

t = years since 1950	P = patents
0	4718
10	2543
20	3214
30	3949
40	8024
50	17,413
60	22,799

(a)Use exponential regression to model P as a function of t.

P(t)

(c)In what years were there more patents awarded than might be expected from the model? (Enter your answers as a comma-separated list.

2. For this exercise, round all regression parameters to three decimal places. The table below shows the average cost C, in dollars, of chemistry and physics periodicals t years after 1980.

t = years since 1980	C = cost in dollars
0	140
5	250
10	410
15	780
20	1300
22	1520

(a) Make an exponential model of C as a function of t.

(c) What was the yearly percentage growth rate of the cost of chemistry and physics periodicals? (Use the model found in part (a). Round your answer to one decimal place.) % (d) If this exponential trend continues, what will be the expected average cost of physics and chemistry periodicals in 2025? Round your answer to the nearest dollar. (Use the model found in part (a).) $

3. For this exercise, round all regression parameters to three decimal places. The following table shows the median income, in thousands of dollars, of American families for 2003 through 2008.

Year	Income (thousands of dollars)
2003	52.68
2004	54.06
2005	56.19
2006	58.41
2007	61.36
2008	61.52

(b) Use exponential regression to construct an exponential model for the income data. (Let t be years since 2003 and H be the median household income in thousand of dollars.

(c) What was the yearly percentage growth rate in median family income during this period? (Use the model found in part (b). Round your answer to one decimal place.) % (d) From 2003 through 2008, inflation was about 3% per year. Did median family income keep pace with inflation during this period? 4. For this exercise, round all regression parameters to three decimal places. Astronomers measure brightness of stars using both the absolute magnitude, a measure of the true brightness of the star, and the apparent magnitude, a measure of the brightness of a star as it appears from Earth. The difference between apparent and absolute magnitude should yield information about the distance to the star. The table below gives magnitude difference m and distance d, measured in light-years, for several stars.

Star	Magnitude difference m	Distance d
Algol	2.56	105
Aldebaran	1.56	68
Capella	0.66	45
Canopus	2.38	98
Pollux	0.13	35
Regulus	2.05	84

(c) If one star shows a magnitude difference 1 greater than the magnitude difference that a second star shows, how do their distances from Earth compare? (Use the model found in part (b).)The star with the larger magnitude difference is times as far away as the other star. (d) A star shows a magnitude difference of 1.46. How far is this star from Earth? (Use the model found in part (b). Round your answer to three decimal places.) light-years (e) A star is 52 light-years from Earth and has an apparent magnitude of 2.47. Find the absolute magnitude of this star. (Use the model found in part (b). Round your answer to three decimal places.) 11. Use exponential regression to fit the following data set. (Round your answers to two decimal places.)

x	4	11	15	17	18
y	1.0	17.3	87.6	197.1	295.6

Use the model found above to calculate y(6). y(6) = Solve y = 250 for x. x =