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)) = (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

Step-by-step explanation:

Given that:

`N_((T)) = (8e^(4T)-2T+5)/(7+2e^(4T))`

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

`N(T) = (8-(2T)/(e^(4T))+(5)/(e^(4T)))/(2+ (7)/(e^(4t)))`

where T is less than
`e^(4T)` ; which is written as :

`T< e^(4T)`

∴
`\lim_(T \to \infty) N(T )= (8-2 \lim_(T \to \infty) (T)/(e^(4T)) +5 \lim_(T \to \infty) (1)/(e^(4T)) )/(2+7 \lim_(T \to \infty) (1)/(e^(4t)) )`

=
`(8)/(2)[ \lim_(T \to \infty) (T)/(e^(4T)) =0 ; \lim_(T \to \infty) (1)/(e^(4t)) }=0]`

where;
`[ \lim_(T \to \infty) (T)/(e^(4T)) =0 \ \ \ and \ \ \lim_(T \to \infty) (1)/(e^(4t)) } = 0]`

Then,
`= (8)/(2)`

= 4

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