Question

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(0.78)^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:
$ square
value after 11 years:
$ square

Explanation:

Step1: Find initial value (t=0)

Substitute $t=0$ into $v(t)$:
$v(0)=25,900(0.78)^0$
Since any number to the power of 0 is 1, $v(0)=25,900\times1=25,900$

Step2: Find value after 11 years

Substitute $t=11$ into $v(t)$:
$v(11)=25,900(0.78)^{11}$
First calculate $(0.78)^{11}\approx0.0560$
Then $v(11)\approx25,900\times0.0560=1450.4$
Round to nearest dollar: $1450$

Answer:

Initial value: $\$25900$
Value after 11 years: $\$1450$