Question

try again
your answer is incorrect.

• initial value: your answer is correct. however, a number greater than or equal to 10,000 is usually written with a comma (or commas).
• value after 11 years: your answer is incorrect.

the dollar value ( v(t) ) of a certain car model that is ( t ) years old is given by the following exponential function.
( v(t) = 25,900(0.88)^t )
find the initial value of the car and the value after 11 years.
round your answers to the nearest dollar as necessary.
initial value: $25900
value after 11 years: $6583

Explanation:

Step1: Initial Value (Correct Format)

The initial value occurs at \( t = 0 \). Substitute \( t = 0 \) into \( v(t)=25,900(0.88)^{t} \). Since \( (0.88)^{0}=1 \), \( v(0)=25,900\times1 = 25,900 \). Format with comma: \( \$25,900 \).

Step2: Value after 11 Years

Substitute \( t = 11 \) into \( v(t)=25,900(0.88)^{11} \). Calculate \( (0.88)^{11} \approx 0.2541 \) (using calculator). Then \( v(11)=25,900\times0.2541 \approx 25,900\times0.2541 \approx 6,581.19 \), round to nearest dollar: \( \$6,581 \).

Answer:

Initial value: \(\$25,900\)
Value after 11 years: \(\$6,581\)