3.7 Applications HW Ans.

7. You drop a ball from a height of 66 inches and the ball starts bouncing. After each bounce, the ball reaches a height that is 80% of the previous height. Write a rule for the height of the ball after the nth bounce. Then find the height of the ball after the sixth bounce.

y = a(1 – r)n

y = 66(0.8)6

y ≈ 17.3

The height of the ball after the sixth bounce is approximately 17.3 inches.

8. The euro is the unit of currency for the European Union. On a certain day, the number of euros, E, which could be obtained for D dollars, was given by this function: E = 0.81419D. Find the inverse of this function, then use the inverse to find the number of dollars that could be obtained for 250 euros on that day.

Inverse:

81419.0

ED

81419.0

250D

250 Euros is approximately $307.05

Let E = 250

9. From 2002 to 2007, the number n (in millions) of blank DVDs a company sold can be modeled by n = 0.42(2.47)t where t is the number of years since 2002. Identify the initial amount, the growth factor, and the annual percent increase. How many DVD’s were sold in 2006?

• The initial amount is 0.42 million DVDs• The growth factor is 2.47• The annual percent increase is 147% y = 0.42(1 + 1.47)t

n = 0.42(2.47)4

15.63 million DVDs were sold in 2006

10. Your sister tells you a secret. You see no harm in telling two friends. After this second passing of the secret, 4 people now know the secret. If each of these people tell 2 new people, after the 3rd passing 8 people will know. If this pattern continues, how many people will know the secret after 10 passings?

1 2 3 4 n2 4 8 16 2n

210 = 1024

1024 people will know after 10 passings.

11. The number of wolves in the wild in the northern section of Cataragas County is decreasing at the rate of 3.5% per year. Your environmental studies class has counted 80 wolves in the area. If this rate continues, how many wolves will remain after 50 years?

y = a(1 – r)n

y = 80(1 – 0.035)50

y = 13.47

Approximately 13 wolves remain after 50 years.