Question

PLEASE HELP ME!!

The population of a certain species of bird in a region after t years can be modeled by the function , where t ≥ 0. When will the population reach 1,200? Question 5 options: about 10 years about 28 years about 35 years about 42 years

Answer 1

The population will reach 1200 after about 2.8 years

Explanation:

The question is incomplete. Here is the complete 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-0.42t , where t ≥ 0. When will the population reach 1,200?

According to question we are to calculate the time t that the population P(t) will reach 1200.To do this we will substitute P(t) = 1,200 into the equation and calculate for the time 't'.

Given;

`P(t) = (1620)/(1+1.15e^(-0.42t) ) \\\\at \ P(t)= 1200;\\\\1200 = (1620)/(1+1.15e^(-0.42t) )\\\\cross\ multiplying\\\\1+1.15e^(-0.42t) = (1620)/(1200) \\\\1+1.15e^(-0.42t) = 1.35\\\\1.15e^(-0.42t) = 1.35-1\\\\e^(-0.42t) = (0.35)/(1.15)\\ \\e^(-0.42t) = 0.3043\\\\Taking \ ln\ of\ both\ sides\\\\lne^(-0.42t) = ln0.3043\\\\-0.42t = -1.1897\\\\t = (-1.1897)/(-0.42) \\\\t = 2.8 years\\\\`

The population will reach 1200 after about 2.8 years