Suppose that the dollar value \( v(t) \) of a certain car that is \( t \) years old is given by the following exponential function. \[ \begin{array}{l}v(t)=29,900(0.91)^{t} \\ \text { Find the initial value of the car. } \\ \text { Does the function represent growth or decay? } \\ \text { O growth } \quad \text { O decay } \\ \text { By what percent does the value of the car change each year? } \\ \square \%\end{array} \]

The initial value of the car can be found by evaluating \( v(t) \) at \( t = 0 \). Plugging in 0 gives us: \[ v(0) = 29,900(0.91)^{0} = 29,900 \times 1 = 29,900. \] This means the initial value of the car is $29,900. Now, onto the nature of the function! Since the base of the exponential function, \( 0.91 \), is less than 1, this indicates that the value of the car is decreasing over time. Therefore, this function represents decay. To find the percent change in the car’s value each year, we can calculate: \[ \text{Percent Change} = (1 - 0.91) \times 100\% = 0.09 \times 100\% = 9\%. \] So, the value of the car decreases by 9% each year.