Question

Your bike was originally purchased for $1,200. it loses about 8% of its original value each year. how many years have passed if the bike is now worth $479.56?

Answer 1

11 years

Explanation:

N = A (1 + increase) ^n

Where N is future amount, A is initial amount, increase is percentage increase/decrease, n is number of mins/hours/days/months/years.

479.56 = 1200(1-0.08)^n

479.56 = 1200 (0.92)^n

0.92^n = (479.56/1200)

takes logs for both sides:

log 0.92^n = log (479.56/1200)

simplify:

n log 0.92 = log (479.56/1200)

n = log (479.56/1200) ÷ log 0.92

= 11.

it will take 11 years for the value to be $479.56