Question

Shiyun bought a car in 1999. The value of the car V , in USD, is depreciating according to the exponential model
V =25000×1.5−0.2t,t⩾0
where t is the time, in years, that Shiyun has owned the car.
a. Write down the value of the car when Shiyun bought it.
b. Calculate the value of the car three years after Shiyun bought it. Give your answer correct to two decimal places.
c. Calculate the time for the car to depreciate to half of its value since Shiyun bought it.
I need c ASAP

Answer 1

Hi there

a) the value of the car is 25000

b) v=25,000×1.5^(−0.2×3)=19,601

C) 12500=25000×1.5^(-0.2t)
Solve for t
12500/25000=1.5^(-0.2t)
Log (12500/25000)=-0.2t×log (1.5)
-0.2t=Log(12500/25000)÷log (1.5)
T=(log(12,500÷25,000)÷log(1.5))÷(−0.2)
T=8.55 years

Hope it helps