Calculus Application Question

[as_xoxo]

Can someone tell me how to do this question? I have attempted it and found an equation, but I don't know if it is right.

Fix N(0) = 10 and r = 2. Suppose that the carrying capacity is dependent upon the amount of nutrients s within the environment. In particular, the carrying capacity is given by the function
K(s) = 5e^2n + 10.
Determine the population density N(s) at fixed time t = 100 as a function of the amount of nutrients s. (Hint: Substitute K(s) for K in the original equation.)

The original equation is:
N(t) = K/(1+(( K/N(0)) −1)e^−rt)

K and r are positive constants


What I did:

I subbed in t=100 and all other information and got the equation.

N(s) = [5e^2s +10] / [1 + ({(5e^2s +10)/10} -1)e^-200]
expanding the denominator and cancelling terms out left me with a final equation of:

N(s) = 10(e^2s + 2)/ (2+e^2s *e^-200)

 

[mmm4444bot]

Fix N(0) = 10 and r = 2

K(s) = 5e^(2n) + 10

N(t) = K/(1 + (K/N(0) − 1) e^(−rt))

K and r are positive constants


What I did:

N(s) = 10(e^(2s) + 2)/(2 + e^(2s)*e^(-200))

K is not a constant; K is a function of s.

(Your exponent 2n looks like a typo.)

Note the red grouping symbols around exponent expressions.

Your result for N(s) looks good. In the denominator, you may simplify the product e^(2s)*e^(-200).

Cheers :cool:

 

[Deleted member 4993]

Can someone tell me how to do this question? I have attempted it and found an equation, but I don't know if it is right.

Fix N(0) = 10 and r = 2. Suppose that the carrying capacity is dependent upon the amount of nutrients s within the environment. In particular, the carrying capacity is given by the function
K(s) = 5e^2n + 10.
Determine the population density N(s) at fixed time t = 100 as a function of the amount of nutrients s. (Hint: Substitute K(s) for K in the original equation.)

The original equation is:
N(t) = K/(1+(( K/N(0)) −1)e^−rt)

K and r are positive constants


What I did:

I subbed in t=100 and all other information and got the equation.

N(s) = [5e^2s +10] / [1 + ({(5e^2s +10)/10} -1)e^-200]
expanding the denominator and cancelling terms out left me with a final equation of:

N(s) = 10(e^2s + 2)/ (2+e^2s *e^-200)

What is 'n'?

What is ''? Cannot decipher!