use logarithm to solve

Question

A car depreciated at 15% per year. How long is it until it is worth half the original value?

Answer 1

each year the value is 0.85 as much. So, after t years it is worth .85^t as much. So, you want t when

.85^t = 0.5

Now take the log of both sides:

t log .85 = log .5
t = (log .5)/(log .85) = 4.26

Answer 2

An automobile depreciates by 23% per year. How soon will it be worth only half its original value?