Question

suppose a new car that cost 20 000 depreciates by 15% each year. in how many year till the car costs 7500. use the equation 7500=(20,000)(0.85)^x

Answer 1

First we can simplify a bit by dividing by 2500:

3 = 8 * (0.85)^x => 0.85^x = 3/8

next, we can take the log() on both sides, and use the fact that log(a^b)=b*log(a)

log(3/8) = log(0.85^x) => log(3/8) / log(0.85) = x

If you calculate this, you find x ≈ 6.03