Question

BRAINLIESTTT ASAP! PLEASE HELP ME :)

Answer 1

Answer:

P=1620

Third option

Step-by-step explanation:

Horizontal Asymptotes

A given function is said to have a horizontal asymptote in y=a, if:  

$\displaystyle \lim _{x\rightarrow -\infty }f(x)=a$

Or,

$\displaystyle \lim _{x\rightarrow +\infty }f(x)=a$

For the given function, the population of the species of bird is given by :

$\displaystyle p(t)=\frac{1620}{1+1.15e^{-0.042t}}$

Where t is the time in years. To find the horizontal asymptote, we should compute both limits to check if they exist.  

$\displaystyle \lim _{x\rightarrow +\infty }\frac{1620}{1+1.15e^{-0.042t}}=\frac{1620}{1+0}=1620$

When t tends to plus infinity, P tends to 1620 .

The second asymptote is computed by:

$\displaystyle \lim _{x\rightarrow -\infty }\frac{1620}{1+1.15e^{-0.042t}}=\frac{1620}{1+\infty}=0$

When t tends to minus infinity, P tends to zero. Since the domain of P is $t\geq 0$, this asymptote is not valid, thus our only asymptote is

$\boxed{P=1620}$