A biology class at high school predicted that a local population of animals will double in size every 12…
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?
P = 12 + 50n
P = 50 + 12n
$P = 50(2)^{12n}$
$P = 50(2)^{n/12}$
Solution
The population doubles every 12 years from an initial 50. After n years the number of doublings is $n/12$, so $P = 50 \times 2^{n/12}$. Checking: at $n = 12$, $P = 50 \times 2^{12/12} = 50 \times 2 = 100$, which is correct. Hence option (d).