Question

The population of a certain species of bird in a region after t years can be modeled by the function P(t)= 1620/1+1.15e^-0.042t , where t ≥ 0. What is the maximum population of the species in the region?
A. 1,620
B. 1,200
C. 0
D. 720

Answer 1

Answer:

A.1620

Step-by-step explanation:

We are given that

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

$t\geq 0$

We have to find the maximum population of the species in the region.

We know that

In fraction

Larger the denominator smaller the value of fraction.number.

Substitute t=0

$P(0)=\frac{1620}{1+1.15e^0}=\frac{1620}{1+1.15}=753.5$

$P(t)=\lim_{t\rightarrow \infty}\frac{1620}{1+1.15e^{-0.042t}}=\frac{1620}{1+0}=1620$

When t increases then the values of $e^{-0.042t}$ decreases

As the denominator decreases the value of given function increases.

The maximum population of the species in the region=1620

A.1620

Answer 2

Answer:

A

Step-by-step explanation:

The function is  $\frac{1620}{1+1.15e^{-0.042t}}$

To find the maximum population, we need to set t towards infinity to get our answer.

So, we replace time with maximum ($\infty$). Let's check:

$\frac{1620}{1+1.15e^{-0.042t}}\\=\frac{1620}{1+\frac{1.15}{e^{0.042t}}}\\=\frac{1620}{1+\frac{1.15}{e^{0.042(\infty)}}}\\=\frac{1620}{1+\frac{1.15}{\infty}}\\=\frac{1620}{1+0}\\=\frac{1620}{1}\\=1620$

The population of birds approaches 1620 as t goes towards infinity. So we can say the max population of the species is 1620.

Correct answer is A