Question

1) For tax purposes a manufacturer is allowed to depreciate the value of a machine by 10% each year. If the original value of the machine was $10,000, what would be its value for tax purposes at the end of 6 years. (Assume the depreciation is computed at the end of each year.)

2) A ball is dropped from a height of 30 feet and rebounds 2/3 of the distance it falls on each bounce. How far has the ball traveled vertically when it hits the ground the 4th time? How far will it travel vertically before coming to a halt? (The convergent value of the infinite sums.)

Answer 1

10000 * 0.9^6

On the nth bounce it has to go a round trip, of height

30*(2/3)^n,
So we want the 1st 4 terms of a G.P. with
a = 30
r = 2/3

30 + 2*S4 = 30+2*30(1 - (2/3)^4)/(1-2/3) = 174.44 ft

Answer 2

174.44 feet😊