Given:
The value of cat v(t) that is t years old is given by the exponential function.
[tex]v(t)=24,500(0.80)^t[/tex]
Required:
Find the value of the car after 7 years and after 12 years.
Explanation:
Substitute t = 7 in the given function.
[tex]\begin{gathered} v(7)=24,500(0.80)^7 \\ v(7)=24,500\times0.2097152 \\ v(7)=5138.0224 \\ v(7)=5183.02 \end{gathered}[/tex]
After 7 years the value of the car is $5138.02
Substitute t = 12 in the given function.
[tex]\begin{gathered} v(12)=24,500(0.80)^{12} \\ v(12)=24,500\times0.0687194767 \\ v(12)=1683.62717 \\ v(12)\approx1683.62 \end{gathered}[/tex]
After 7 years the value of the car is $ 1683.62
Final answer:
The value of the car after 7 years and 12 years is $5138.02 and $ 1683.62.
