The initial value of car is $24,000. After one year the value of the car...

Given data is :
The initial (t=0) value of the car is $24000
After one year (t=1) the value of the car is $19350
Let exponential model is ${\displaystyle f\left(t\right)=A{e}^{kt}}$
At t=0,
${\displaystyle f\left(0\right)=24000}$
${\displaystyle A{e}^0=24000}$
${\displaystyle A=24000}$
After 1 years t=1
${\displaystyle f\left(1\right)=19350}$
${\displaystyle A{e}^{k\times 1}=19350}$
${\displaystyle 24000e^k=19350}$
${\displaystyle k=-0.2153}$
Substitute value A and k in f(t)
${\displaystyle f\left(t\right)=24000e^{-0.2153t}}$
Cost after 4 years is
$f(4)=\$24000e^{-0.2153t}$
${\displaystyle =\mathrm{\$}10143.71}$
${\displaystyle \approx \mathrm{\$}10144}$
Thus, the cost of a car after 4 years is $10144