Population Growth

[nycmathguy]

Section 2.6
Question 70

What is Part (c) asking for?

 

[MathLover1]

a.

b. just plug in given values

c. you have to find a limit

 

[nycmathguy]

a.

View attachment 513


b. just plug in given values

c. you have to find a limit

I can easily do part (b). Part (c) involves calculus which I have not studied. I know the basics of finding limits but not as x tends to infinity. How is part (c) done? Do I replace every x with infinity and simplify the algebraic fraction?

 

[MathLover1]

no, you cannot replace every x with infinity and simplify the algebraic fraction
that way would be infinity/infinity

so, you have to use limits

 

[MathLover1]

you can do limiting like this
as t ---> infinity large number
n = (100 + 60(infinity))/(1 + .04*infinity)

since (100 + 60(infinity)) is approximately 60(infinity) and (1 + .04*infinity) is .04*infinity
approximately = 60(infinity)/.(04*infinity)=60/.04 ---> 1500
the limiting size = 1500

example: let t = 100,000
N = 20(5+300000)/(1 + 4000) = 1499.650

 

[nycmathguy]

you can do limiting like this
as t ---> infinity large number
n = (100 + 60(infinity))/(1 + .04*infinity)

since (100 + 60(infinity)) is approximately 60(infinity) and (1 + .04*infinity) is .04*infinity
approximately = 60(infinity)/.(04*infinity)=60/.04 ---> 1500
the limiting size = 1500

example: let t = 100,000
N = 20(5+300000)/(1 + 4000) = 1499.650

I will leave this calculus stuff for next year after our precalculus journey.

 

[nycmathguy]

a.

View attachment 513


b. just plug in given values

c. you have to find a limit

Part (b)

Let N = deer population

When t = 5, N = 333.3.

When t = 10, N = 500.

When t = 25, N = 800.