Find a logistic function that describes the given population. Then

Marenonigt 2021-12-29 Answered
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.)
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Expert Answer

Bob Huerta
Answered 2021-12-30 Author has 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)

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abonirali59
Answered 2021-12-31 Author has 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

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Vasquez
Answered 2022-01-09 Author has 460 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

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