Question

The dollar value of a car is a function f, . of the number of years, t, since the car was purchased. Thefunction is defined by the equations f(t) = 12000*(3/5)^ta. What does the 12,000 tell us about the situationb. What does the 3/5tell us about the situation?C.What will be the value of the car after 3 years?

Answer 1

Given the following question:

$f(t)=12000\times(\frac{3}{5})^t$

Part A:

I believe that the 12,000 tells us the orginal price of the car, or the price the car was purchased for. 12000 is the orginal price of the car.

Part B:

I believe that the 3/5 tells us the decline in value each year after the car has been purchased. Which is why t is the exponet is t was 2 you would have to multiply 3/5 by itself twice and then multiply it by 12000 which further decreases it's value. 3/5 represents the decline in value after T years.

Part C:

t = number of years

t = 3

$\begin{gathered} f(t)=12000\times\frac{3}{5^{}}^3 \\ \frac{3}{5}^3=\frac{3}{5}\times\frac{3}{5}\times\frac{3}{5} \\ \frac{3}{5}\times\frac{3}{5}=\frac{9}{25} \\ \frac{9}{25}\times\frac{3}{5}=\frac{27}{125} \\ 12000\times\frac{27}{125}=2592 \\ v=2592 \end{gathered}$

Value of the car after three years will be 2592.