The rate of growth of a certain cell culture is proportional to its size. In 8 hours a population of 1 million cells grew to 5 million. How large will the cell culture be after 12 hours?
The population of the cell culture after 12 hours will be $\square$ million. (Round the final answer to the nearest million as needed. Round all intermediate values to the nearest thousandth as needed.)

Step 1 ：Given that the initial population (P0) is 1 million cells and after 8 hours the population (P8) grew to 5 million cells. We are asked to find the population after 12 hours (P12).

Step 2 ：This is a problem of exponential growth. The formula for exponential growth is \(P(t) = P0 * e^{rt}\), where \(P(t)\) is the final population, \(P0\) is the initial population, \(r\) is the rate of growth, and \(t\) is the time.

Step 3 ：First, we need to find the rate of growth \(r\). We can do this by rearranging the formula to solve for \(r\): \(r = \ln(P(t)/P0) / t\).

Step 4 ：Substituting the given values into the formula, we get \(r = \ln(5/1) / 8 = 0.20117973905426254\).

Step 5 ：Now that we have \(r\), we can substitute it back into the formula to find \(P(12)\).

Step 6 ：Substituting the values into the formula, we get \(P(12) = 1 * e^{0.20117973905426254 * 12} = 11.180339887498945\).

Step 7 ：Rounding to the nearest million, we get \(P(12) = 11\) million.

Step 8 ：Final Answer: The population of the cell culture after 12 hours will be \(\boxed{11}\) million.