A rubber ball is dropped onto a hard surface from a height of 6 feet, and it bounces up and down….

A rubber ball is dropped onto a hard surface from a height of 6 feet, and it bounces up and down. At each bounce it rises to 90% of the height from which it fell.

(a) Find a formula for h(n), the height reached by the ball on bounce n.

(b) How high will the ball bounce on the 12th bounce?

(c) How many bounces before the ball rises no higher than an inch?

Oil leaks from a tank. At hour t = 0 there are 250 gallons of oil in the tank. Each hour after that, 4% of the oil leaks out.

(a) What percent of the original 250 gallons has leaked out after 10 hours? Why is it less than 10 · 4% = 40%?

(b) If Q(t) = Q0ekt is the quantity of oil remaining after t hours, find the value of k. What does k tell you about the leaking oil?

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