Question

Suppose that the dollar value v(t) of a certain car that is t

Answer 1

`\begin{gathered} \text{Given} \\ v(t)=25900(1.25)^t \end{gathered}`

Part A: Finding the initial value of the car

Substitute t = 0 to the given function and solve for v(t)

`\begin{gathered} v(t)=25900(1.25)^t \\ v(0)=25900(1.25)^0 \\ v(0)=25900(1) \\ v(0)=25900 \end{gathered}`

Therefore, the initial value of the car is $25,900.

Part B: Growth or Decay

Since the base of the exponential function is greater than 1, in this case 1.25, the function represents growth.

Part C: Percent change every year

Subtract 1 from the base 1.25, and multiply by 100%

`\begin{gathered} 1.25-1=0.25 \\ \\ 0.25\cdot100\%=25\% \end{gathered}`

Therefore, the percent change each year is 25%.