Trent Carpenter

2021-09-19

The initial value of car is $24,000. After one year the value of the car is$19,3550. What exponential dunction models the expected value of the car? Estimate the value of the car after 4 years.

### Answer & Explanation

Roosevelt Houghton

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 $f\left(t\right)=A{e}^{kt}$
At t=0,
$f\left(0\right)=24000$
$A{e}^{0}=24000$
$A=24000$
After 1 years t=1
$f\left(1\right)=19350$
$A{e}^{k×1}=19350$
$24000{e}^{k}=19350$
$k=-0.2153$
Substitute value A and k in f(t)
$f\left(t\right)=24000{e}^{-0.2153t}$
Cost after 4 years is
$f\left(4\right)=24000{e}^{-0.2153t}$
$=\mathrm{}10143.71$
$\approx \mathrm{}10144$
Thus, the cost of a car after 4 years is \$10144

Do you have a similar question?

Recalculate according to your conditions!