The dollar value $v(t)$ of a certain car model that is $t$ years old is given by the following exponential function.
\[
v(t)=26,000(0.80)^{t}
\]
Find the initial value of the car and the value after 10 years.
Round your answers to the nearest dollar as necessary.
Initial value:
Value after 10 years:
\[
\times \quad 5
\]
Explration
Check
Answer
\boxed{\text{Initial value: } $26,000 \text{, Value after 10 years: } $2,792}
Step 1 ：Find the initial value of the car by evaluating the function at t=0: \(v(0) = 26,000(0.80)^{0}\)
Step 2 ：Find the value of the car after 10 years by evaluating the function at t=10: \(v(10) = 26,000(0.80)^{10}\)
Step 3 ：Calculate the values: \(v(0) = 26,000\) and \(v(10) \approx 2,792\)
Step 4 ：\boxed{\text{Initial value: } $26,000 \text{, Value after 10 years: } $2,792}
