\begin{tabular}{l} Suppose that the dollar value \( v(t) \) of a certain car that is \( t \) years old is given by the following exponential function. \\ \( v(t)=19,900(1.22)^{t} \) \\ \begin{tabular}{|l|}\hline Find the initial value of the car. \\ \hline Does the function represent growth or decay? \\ O growth o decay \\ \hline By what percent does the value of the car change each year? \\ \( \square \% \)\end{tabular} \\ \hline\end{tabular}

The initial value of the car, when \( t=0 \), can be found by substituting 0 into the function \( v(t) = 19,900(1.22)^{t} \). This gives us \( v(0) = 19,900(1.22)^0 = 19,900(1) = 19,900 \). So, the initial value of the car is $19,900. The function represents growth because the base of the exponent, \( 1.22 \), is greater than 1. Specifically, this means that the value of the car increases as time progresses. To find the percent change each year, we can calculate it as \( (1.22 - 1) \times 100 = 22\% \). Therefore, the value of the car increases by 22% each year!