the price of a car depricates over time at a rate of approximately 18% according to the formula (C)t=36,500(0.82)^t. what was the inital cost of the car? what will the car be worth in 4 years? when will the car be worth less than 5,000?

Answer 1

a. C(t) = 36,500(0.82)^0 = $36,500.

b. C(t) = 36500(0.82)^4 = $16,502.44.

c. 36,500(0.82)^t = $5000.
(0.82)^t < 5000 / 36500.
(0.82)^t = 0.1370.
t*Log(0.82) = Log(0.1370).
t = Log(0.1370) / Log(0.82).
t = 10 yrs.