Find a logistic function that describes the given population. Then

Marenonigt

Marenonigt

Answered question

2021-12-29

Find a logistic function that describes the given population. Then graph the population function. The population increases from 300 to 700 in the first year and eventually levels off at 5400. Write the equation of a logistic function that models the given population. P(t)= (Type an exact answer.)

Answer & Explanation

Bob Huerta

Bob Huerta

Beginner2021-12-30Added 41 answers

Population increases 300 to 700
levels off at 5400.
Logistic equation is given by
P(t)=L1+A×eB(t)
B=1f1×ln(P0(P5P1)P1(P5P0))]
P0initial population
P1after(f1)population
P5level of population
B=ln[300(5400700)700(5400300)]
B=ln[300×4700700×5100]=ln[47119]
at t=0P0=300
300=54001+Axe01+A=5400300=18
A=181=17
P(t)=54001+(7)eln(47119t)
abonirali59

abonirali59

Beginner2021-12-31Added 35 answers

The logistic equation has general form
f(x)=L1+AeBx (1)
L=5400, here x is to find A and B
P0=initial population
P1=aftert1population
P5=level of population
from equation (1)
B=ln[300(5400700)700(5400300)]=ln[300×4700700×5100]
B=ln[47119]
After getting a put t, to find A
54001+A=300
1+A=18
A=17

Vasquez

Vasquez

Expert2022-01-09Added 669 answers

b(t)=c1+AeBt, where c is canuing capacityandB=1t1ln(P0(P5P1)P1(P5P0)) and A=cP0P0Given that, at t=0,P0=300t=1,P1=700P5=5400As P(t)=c1+AeBt, here c=5400And B=1f1ln(P0(P5P1)P1(P5P0))=11ln(300(5400700)700(5400300))=ln(47119)A=5400300300=5100300=17=54001+477t

Do you have a similar question?

Recalculate according to your conditions!

New Questions in Differential Equations

Ask your question.
Get an expert answer.

Let our experts help you. Answer in as fast as 15 minutes.

Didn't find what you were looking for?