ANSWER :
5.9 years
EXPLANATION :
Exponential function can be expressed as :
[tex]y=A(1\pm r)^t[/tex]where A = initial amount
r = (+) growth or (-) decay rate
t = time
y = amount after t years
From the problem, the initial value of the car is A = $32,500
It depreciates at a rate of 11.1% annually, so r = -11.1% or -0.111
The value of the car will be 50% of its original value, so y = 0.50(32,500) = $16,250
Using the formula above :
[tex]\begin{gathered} 16250=32500(1-0.111)^t \\ \frac{16250}{32500}=(0.889)^t \\ \\ 0.5=(0.889)^t \\ \text{ Take the ln of both sides :} \\ \ln(0.5)=\ln(0.889)^t \\ \ln(0.5)=t\ln(0.889) \\ \\ t=\frac{\ln0.5}{\ln0.889}=5.89\sim5.9yrs \end{gathered}[/tex]