Respuesta :
The population of fish in a certain lake follows the logistic growth function
[tex] f(x)= \frac{25000}{1+8.25e^{-0.076t}} [/tex]
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)
[tex] f(x)= \frac{25000}{1+8.25e^{-0.076*20}} [/tex]
=8914.65
The population after 20 years = 8914.65
Answer:
The population will be approx 8915.
Step-by-step explanation:
The population of fish in a certain lake follows the logistic growth function -
[tex]f(t)=\frac{25000}{1+8.25e^{-0.076t} }[/tex]
We have to find the population when t = 20
[tex]f(20)=\frac{25000}{1+8.25e^{-0.076(20)} }[/tex]
=> [tex]\frac{25000}{1+8.25e^{-1.52} }[/tex]
=> [tex]\frac{25000}{1+8.25(0.21871188)}[/tex]
=> [tex]\frac{25000}{1+1.8044}[/tex]
=> [tex]\frac{25000}{2.8044}[/tex]
= 8914.56 or approx 8915.
The population will be approx 8915.
