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)
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)
Last edited: