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3.7 Applications HW Ans.

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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 n th 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.

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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: 250 Euros is approximately $307.05 Let E = 250

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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

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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 3 rd passing 8 people will know. If this pattern continues, how many people will know the secret after 10 passings? 1234n 248162n2n 2 10 = 1024 1024 people will know after 10 passings.

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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.

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