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:
$\times 5$
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Answer

\boxed{\text{Initial value: } $26, 000, Value after 10 years:$ 2,792}

Steps

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: } $26, 000, Value after 10 years:$ 2,792}