\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}

**Step 1: Find the initial value of the car.** The initial value is found by evaluating the function at \( t=0 \): \[ v(0)=19,\!900\,(1.22)^0=19,\!900\,(1)=19,\!900. \] Thus, the initial value is \(\$19,\!900\). **Step 2: Determine if the function represents growth or decay.** The function is given by \[ v(t)=19,\!900\,(1.22)^t. \] Since the base \( 1.22 \) is greater than 1, the function represents exponential **growth**. **Step 3: Find the percent change each year.** An exponential function of the form \[ v(t)=\text{initial value}\,(r)^t \] indicates that the value changes by a factor of \( r \) each year. Here, \( r=1.22 \). This means that each year, the value of the car increases by a factor of \( 1.22 \), i.e., there is a \( 1.22 - 1 = 0.22 \) increase relative to the previous year. Converting this to a percentage: \[ 0.22 \times 100\%=22\%. \] Thus, the car’s value increases by **22\%** each year.