A biology class at high school predicted that a local population of animals will double in size every 12 years. The population at the beginning of the year 2021 was estimated to be 50 animals. If P represents the population after n years, then which one of the following equations represents the model of the class for the population?

The correct answer is $P=50{\left(2\right)}^{\frac{n}{12}}$.

To find the equation representing the animal population growth model, let us analyze the given information step-by-step:

1. Identify the Initial Population:
The initial population at the beginning of the year 2021 (when $n=0$) is given as 50 animals.

2. Understand the Doubling Rate:
The population doubles in size every 12 years. This means the growth factor is 2 every 12-year time block.

3. Formulate the Exponential Growth Model:
The general exponential growth formula is given by:

$P=P_0{\left(b\right)}^{\frac{n}{t}}$

where:
• $P$ is the population after $n$ years.
• $P_0=50$ is the initial population.
• $b=2$ is the growth factor (since the population doubles).
• $t=12$ is the time interval in years required for the population to double.
• $n$ is the total number of years elapsed.

4. Substitute the Values:
Substituting these values into the formula gives:

$P=50{\left(2\right)}^{\frac{n}{12}}$

This equation correctly models the animal population after $n$ years.