\begin{tabular}{l} A study is done on the number of bacteria cells in a petri dish. Suppose that the population size \( P(t) \) after \( t \) hours is given \\ by the following exponential function. \\ \( P(t)=2200(1.04)^{t} \) \\ Find the initial population size. \\ \hline \( \begin{array}{c}\text { Does the function represent growth or decay? } \\ \text { O growth o decay }\end{array} \) \\ \hline By what percent does the population size change each hour? \\ \hline\end{tabular}

The initial population size is found by evaluating the function at \( t = 0 \). Plugging in, we get \( P(0) = 2200(1.04)^{0} = 2200 \). So, the initial population size is **2200 bacteria cells**. The function \( P(t) \) represents growth because the base of the exponent, \( 1.04 \), is greater than 1. This indicates that the population is increasing over time. The percent change in population size each hour can be calculated using the formula for percentage increase: \( (r - 1) \times 100\% \), where \( r \) is the growth factor. In this case, the percent change is \( (1.04 - 1) \times 100\% = 4\% \). Thus, the population size increases by **4% each hour**.