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 2014 was estimated to be 50 animals. If P represents the population n years after 2014. Find the equations represents the class model of the population over time?


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Question Number 175280 by naka3546 last updated on 26/Aug/22

$A biology class at central high school$ $predicted that a local population of animals$ $will double in size every 12 years .$ $The population at the beginning of 2014$ $was estimated to be 50 animals .$ $If P represents the population n years after 2014 .$ $Find the equations represents the class model$ $of the population over time ?$
	Answered by MJS_new last updated on 26/Aug/22

	$P = 50 \times 2^{n / 12}$
	Answered by FelipeLz last updated on 26/Aug/22

	$\frac{d P}{d n} = k P \Rightarrow P (n) = P_{0} e^{k n}$ $P (n + 12) = 2 P (n)$ $P_{0} e^{k (n + 12)} = 2 P_{0} e^{k n}$ $e^{k (n + 12)} = 2 e^{k n}$ $k (n + 12) = \ln (2) + k n$ $12 k = \ln (2) \Rightarrow k = \frac{\ln (2)}{12}$ $P_{0} = 50$ $P (n) = 50 e^{\frac{\ln (2) n}{12}} = 50 \sqrt[12]{2^{n}}$
	Commented by MJS_new last updated on 26/Aug/22

	$50 \sqrt[12]{2^{n}} = 50 \times 2^{n / 12}$
	Commented by naka3546 last updated on 27/Aug/22

	$Thank you, sir .$
	Commented by peter frank last updated on 28/Aug/22

	$thank you$
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