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

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