People Syllabus Modules Google Drive Office 365 A population grows according to an exponential growth model. The initial population is $P_{0}=4$, and the common ratio is $r=1.35$. Then: \[ \begin{array}{l} P_{1}= \\ P_{2}= \end{array} \] Find an explicit formula for $P_{n}$. Your formula should involve $n$. \[ P_{n}= \] Use your formula to find $P_{12}$ \[ P_{12}= \] Give all answers accurate to at least one decimal place

Step 1 ：The problem is asking for an explicit formula for an exponential growth model. The formula for exponential growth is generally given by \(P_n = P_0 * r^n\), where \(P_0\) is the initial population, \(r\) is the common ratio, and \(n\) is the number of time periods.

Step 2 ：In this case, \(P_0 = 4\) and \(r = 1.35\). We can substitute these values into the formula to find \(P_n\).

Step 3 ：The explicit formula for \(P_{n}\) is \(P_{n} = 4 * 1.35^n\).

Step 4 ：After finding the formula for \(P_n\), we can substitute \(n = 12\) to find \(P_{12}\).

Step 5 ：Using this formula, \(P_{12}\) is approximately \(\boxed{146.6}\).