\begin{tabular}{l} Suppose that the future price \( p(t) \) of a certain item is given by the following exponential function. In this function, \( p(t) \) is measured in dollars and \( t \) is \\ number of years from today. \\ \( p(t)=1200(1.039)^{t} \) \\ Find the initial price of the item. \\ \$1200 \\ \hline \( \begin{array}{l}\text { Does the function represent growth or decay? } \\ \text { Browth o decay }\end{array} \) \\ By what percent does the price change each year? \\ \hline\( \% \)\end{tabular}

The initial price of the item when \( t = 0 \) is straightforward: by substituting \( t = 0 \) into the equation \( p(t) = 1200(1.039)^{0} \), we find that \( p(0) = 1200(1) = 1200 \). So, the initial price is indeed \$1200! This function clearly represents growth because the base of the exponential \( 1.039 \) is greater than 1. Specifically, every year, the price increases, indicating a positive change. To find the percentage change each year, subtract 1 from the growth factor and multiply by 100. Thus, the price changes by \( (1.039 - 1) \times 100 = 3.9\% \) each year!