Question

A subpopulation of plant, isolated from the main population, is found to obey the function below, describing the number of individuals (in thousands). N( ) = 8e4 ???? 2 + 5 7 + 2e4 What is the ultimate fate of this subpopulation of plants? Justify your claim with the appropriate mathematics.

Answer 1

Here is the correct format of the equation in the question.

A subpopulation of plant, isolated from the main population, is found to obey the function below, describing the number of individuals (in thousands).

$N_{(T)} = \frac{8e^{4T}-2T+5}{7+2e^{4T}}$

What is the ultimate fate of this subpopulation of plants? Justify your claim with the appropriate mathematics.

Answer:

the ultimate fate of this subpopulation of plants = 4

Explanation:

Given that:

$N_{(T)} = \frac{8e^{4T}-2T+5}{7+2e^{4T}}$

Taking the limit of N(T) ; we have ,$\lim_{T \to \infty} N(T)$

$N(T) = \frac{8-\frac{2T}{e^{4T}}+\frac{5}{e^{4T}}}{2+ \frac{7}{e^{4t}}}$

where T is less than $e^{4T}$ ; which is written as :

$T< e^{4T}$

∴  $\lim_{T \to \infty} N(T )= \frac{8-2 \lim_{T \to \infty} \frac{T}{e^{4T}} +5 \lim_{T \to \infty} \frac{1}{e^{4T}} }{2+7 \lim_{T \to \infty} \frac{1}{e^{4t}} }$

= $\frac{8}{2}[ \lim_{T \to \infty} \frac{T}{e^{4T}} =0 ; \lim_{T \to \infty} \frac{1}{e^{4t}} }=0]$

where; $[ \lim_{T \to \infty} \frac{T}{e^{4T}} =0 \ \ \ and \ \ \lim_{T \to \infty} \frac{1}{e^{4t}} } = 0]$

Then, $= \frac{8}{2}$

= 4

Thus, the ultimate fate of this subpopulation of plants = 4