Question

Brianna bought a new car for $15000. Each year the value of the car deprecaites by 30% of its value of the previous year. In how many years will the car be worth only $500?

Answer 1

A = P(1+r%)ⁿ , where P = initial value, A= new value, n = number of years and
r% is the growth or depreciation rate, depending on its sign:
If it's a depreciation, the formula becomes:

A = P(1 - r%)ⁿ

500 = 15000(1-0.3)ⁿ

500/15000 = (0.7)ⁿ

0.033333 = 0.7ⁿ


ln(0.03333) = n.ln(0.7)

n = ln(0.03333)/ln(0.7)

n = 9.5 years

Answer 2

The formula is
A=p (1-r)^t
A future value 500
P current value 15000
R rate of depreciation 0.3
T time?
500=15000 (1-0.3)^t
Solve for t
Divide both sides by 15000
500/15000=(1-0.3)^t
Take the log for both sides
Log (500/15000)=t×log (1-0.3)
Divide both sides by log (1-0.3)
T=(log(500÷15,000)÷log(1−0.3))
T=9.5 years round your answer to get 10 years

Hope it helps!