Question

The population of fish in a certain lake follows the logistic growth function f(t)=25000/1+8.25e^-0.076 where t is the time in years. According to the growth model, what will the populations be after 20 years

Answer 1

The population of fish in a certain lake follows the logistic growth function

`f(x)= (25000)/(1+8.25e^(-0.076t))`

where t is the time in years. According to the growth model, what will the populations be after 20 years?

We are given with growth model f(x). In that , t represents the time in years.

To find out the population after 20 years, we plug in 20 for t and find out f(20)

`f(x)= (25000)/(1+8.25e^(-0.076*20))`

=8914.65

The population after 20 years = 8914.65

Answer 2

The population will be approx 8915.

Explanation:

The population of fish in a certain lake follows the logistic growth function -

`f(t)=(25000)/(1+8.25e^(-0.076t) )`

We have to find the population when t = 20

`f(20)=(25000)/(1+8.25e^(-0.076(20)) )`

=>
`(25000)/(1+8.25e^(-1.52) )`

=>
`(25000)/(1+8.25(0.21871188))`

=>
`(25000)/(1+1.8044)`

=>
`(25000)/(2.8044)`

= 8914.56 or approx 8915.

The population will be approx 8915.