\begin{tabular}{l} A study is done on the population of a certain fish species in a lake. Suppose that the population size \( P(t) \) after \( t \) years is \\ given by the following exponential function. \\ \( P(t)=530(1.36)^{t} \) \\ Find the initial population size. \\ \( \square \) \\ \hline \( \begin{array}{c}\text { Does the function represent growth or decay? } \\ \text { O growth } \quad \text { O decay }\end{array} \) \\ \hline\( \square \% \) \\ \hline\end{tabular}

1. **Finding the Initial Population** The population function is given by \[ P(t)=530(1.36)^t. \] To find the initial population, we set \( t = 0 \): \[ P(0)=530(1.36)^0=530\cdot1=530. \] Therefore, the initial population size is \(530\). 2. **Determining Growth or Decay** The exponential function \( P(t)=530(1.36)^t \) has a base of \( 1.36 \). Since \( 1.36 > 1 \), the function represents exponential growth. \[ \boxed{530\text{ and growth}} \]