A biology class at Central High School predicted that a local population of animals will double in size every 12 years. The population at the beginning of 2021 was estimated to be 50 animals. If P represents the population n years after 2021, then which of the following equations represents the class model of the population over time?
P = 50 (2) n/12
Given:
Population of animals in the beginning of 2021 = 50
Thereafter the population of animals will double in every 12 years
Calculation:
Since, the population is doubling every 12 years the equation will be exponential such that P = 50 \(×\) (2) x
Now when n = 0, P = 50
We get 50 = 50 × 2 x
⇒ 2 0 = 2 x
⇒ x = 0
when n = 12, P = 100 (as it doubles in 12 years)
So we get 100 = 50 × 2 x
⇒ 2 1 = 2 x
⇒ x = 1
Similarly, n = 24, P = 200 and we get x = 2
So, the relation between x and n is x = n/12 and the equation for the model becomes P = 50 × 2 n/12 .
Hence, option 4 is correct.
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