How do I find the years? without a graphing calculator??

Question

A fully loaded Toyota Forerunner sells for 42,000. It depreciates 12% per year from the date of purchase. How many years will it take to be worth half its purchase price?

I have found this 42,000(1-0.12)^x

42,000(.88)^x

But I have no idea how to find the years that it will take to be worth half its purchase price and the half of 42,000 is 21000...

Answer 1

Your equation is correct.

y=42000(.88)^x Plug in 21000 in for y and solve

21000=42000(.88)^x Divide both sides by 42000 and simplify

21000/42000=42000/42000(.88)^x

0.5=(.88)^x Rewrite this a a logarithm.

log _0.88(0.5)=x

Using the change of base formula

log(0.5)/log(0.88)=x

x=5.42 years