[tex]\begin{gathered} \text{Given} \\ v(t)=25900(1.25)^t \end{gathered}[/tex]
Part A: Finding the initial value of the car
Substitute t = 0 to the given function and solve for v(t)
[tex]\begin{gathered} v(t)=25900(1.25)^t \\ v(0)=25900(1.25)^0 \\ v(0)=25900(1) \\ v(0)=25900 \end{gathered}[/tex]
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%
[tex]\begin{gathered} 1.25-1=0.25 \\ \\ 0.25\cdot100\%=25\% \end{gathered}[/tex]
Therefore, the percent change each year is 25%.
