Question

N(t) = K / (1 + (K - 1)e^-rt) Where r and K are positive constants representing the population growth rate and carrying capacity, respectively. (A) (5) Plot N(t) as a function of time t, t >= 0, for K = 1000, r = 0.02, and K = 2000, r = 0.02. What happens to the population size as time increases? (B) (5) Find the rate of change of the population per unit of time, dN/dt (do not substitute any values for K or r). (C) (10) Note that dN/dt = rN(1 - N/K) (you can check this by substituting N(t) on the right hand side of this equation and simplify until you obtain what you found in part (B)). Plot dN/dt and the per capita rate of growth 1/N * dN/dt, 0 <= N <= 1000, as a function of N, in the same coordinate plane for K = 1000, r = 0.02. What happens to the per capita rate of growth as the population increase?

          N(t) = K / (1 + (K - 1)e^-rt)
Where r and K are positive constants representing the population growth rate and carrying capacity, respectively.
(A) (5) Plot N(t) as a function of time t, t >= 0, for K = 1000, r = 0.02, and K = 2000, r = 0.02. What happens to the population size as time increases?
(B) (5) Find the rate of change of the population per unit of time, dN/dt (do not substitute any values for K or r).
(C) (10) Note that dN/dt = rN(1 - N/K) (you can check this by substituting N(t) on the right hand side of this equation and simplify until you obtain what you found in part (B)).
Plot dN/dt and the per capita rate of growth 1/N * dN/dt, 0 <= N <= 1000, as a function of N, in the same coordinate plane for K = 1000, r = 0.02. What happens to the per capita rate of growth as the population increase?

N(t) = K / (1 + (K - 1)e^-rt)
Where r and K are positive constants representing the population growth rate and carrying capacity, respectively.
(A) (5) Plot N(t) as a function of time t, t >= 0, for K = 1000, r = 0.02, and K = 2000, r = 0.02. What happens to the population size as time increases?
(B) (5) Find the rate of change of the population per unit of time, dN/dt (do not substitute any values for K or r).
(C) (10) Note that dN/dt = rN(1 - N/K) (you can check this by substituting N(t) on the right hand side of this equation and simplify until you obtain what you found in part (B)).
Plot dN/dt and the per capita rate of growth 1/N * dN/dt, 0 <= N <= 1000, as a function of N, in the same coordinate plane for K = 1000, r = 0.02. What happens to the per capita rate of growth as the population increase?

Added by Samuel M.

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