The value of a $20,000 car decreases every, t. The equation below model this situation.

Question

20,000(1-0.04t) = 13,000

How many years will the car be worth $13,000? Round to the nearest tenth if necessary.

I got 20,000(.96t)= 13,000, but I don't believe gives me the correct answer. Help!

Answer 1

this does not make sense:
" decreases every, t "

did it say it decreased 4% per year?
that would mean
.96^n =13/20
.96^n = .65
n log .96 = log .65
n = -.187/-.0177
= 10.6 years

Answer 2

I understand most of the explanation except the part below:

n log .96 = log .65
n = -.187/-.0177

Could you please explain? Thanks