Answer - K = 6000, N= 3000
Here r is per capita growth rate which depends on population size (N) and carrying capacity (N). Here it is assumed that population has a base growth rate of r( max) when it is very small . Since the value of r is very small , for greatest rate the value of K and N will be 6000 and 3000 respectively .
rN dt In the equation for logistic growth, K represents the carrying capacity and N represents...
Exercise 4: Assume that a population is governed by a logistic equation with carrying capacity K intrinsic growth rate r, and initial population size K is subjected to constant effort harvesting: (a) Determine the population size, N(t) (b) Verify that if E< r, the population size will approach the positive steady state, Ni, the carrying capacity K if Erand if E>r, the population will approach the zero steady state, No, astoo. (c) Find the maximum sustainable yield of the population.
Under logistic growth for a population whose carrying capacity is 100, at what population size would you expect the greatest realized per capita growth rate? N-0 Whatever populations made NEK N-1/2
The equation for logistic growth in a particular population is: dN/dt Time is measured in months and biomass is measured in grams. The carrying capacity of the population is? 0.4N(1-N/100 a) 200 grams/year b) 250 grams/year c) 80 grams d) 0.4 grams e) 0.4 grams/year f) 100 grams
1- Assume a pond’s carrying capacity of frogs is 300 and the intrinsic growth rate is 0.3. What is the growth rate of frogs if there are 30 individuals currently present? Hint: dN/dt=rN((K-N)/K). a. 8 b. 5 c. 13 d. 3 2- If a starting population of cicadas is 100, the birth rate per capita is 0.6, the death rate per capita is 0.3, how big will the population of cicadas at 10 years? Hint: Nt=N0ert, r=b-d, and e=2.718. a....
The logistic equation represents the idea that populations first increase exponentially but then their growth decreases as they approach carrying capacity.
dN dt (K-N) The change in population size (dN) per unit time (d),--, is equal to rN. What would be the population change per year (eg, dt = 1 yr) in a population of 5433 individuals, with a per capita growth rate of 0.06, and a carrying capacity of 7606?
What do the K represent in the logistic growth mode formulasl? M= Carrying Capacity DelatP = kP(1-P/M) - Growth k(1-P/M)- Growth Rate
dn n(0)=1 = rn. dt Main activity (2.5 marks) (a) If we modify Eq. *) to model a growing population with an additional con- stant rate of immigration, a, we get dn n(0) = 1. = rn a, dt Solve this using the integrating factor method (b) Another population growth model is the logistic equation dn - гn(1 — п). dt Solve this, with the initial condition n(0) = 1/10 (c) Adding immigration, a, the logistic equation becomes dn —...
1. Describe this equation and what does it mean? When it would be used by an ecologist? dN/dt = rN 2. Describe this equation and what does it mean? When it would be used by an ecologist? dN/dt = r N (1 - N/K) 3 . Describe this equation and what does it mean? When would it be used by an ecologist? Nt = No ert 4. Distinguish between exponential and logistic population growth. Give the equations for each. 5....
3. (17 points) The growth in a population of bacteria follows a logistic growth model given by the differential equation dP 0.05P - 0.00001p? dt with units of number of bacteria and hours. (a) (3 points) What is the carrying capacity of this population? (b) (9 points) Given an initial population of 1000 bacteria, how long will it take for the population to double? (c) (5 points) What is the rate of change (per hour) in the size of the...