Suppose that a country's population is 64 million and its population growth rate is 3.7% per year. If the population growth follows a logistic growth model with r=.053, what is the country's carrying capacity?
http://en.wikipedia.org/wiki/Logistic_function
dp/dt= rP(1-P/K)
You are looking for K, given r, and given dp/dt as .037
Isn't it just some algebra to solve?
To find the carrying capacity of a country's population growth, we need to use the logistic growth model formula. The formula for logistic growth is:
P(t) = K / (1 + A * e^(-r * t))
Where:
P(t) is the population at time t
K is the carrying capacity
A is a constant that determines the initial population size
e is the base of the natural logarithm (approximately equal to 2.71828)
r is the growth rate
t is the time
In this case, we have the following information:
Population = 64 million
Growth rate (r) = 0.053 (5.3% expressed as a decimal)
To find the carrying capacity (K), we need to solve for it using the logistic growth model formula.
1. Start by converting the growth rate from a percentage to a decimal:
r = 0.053
2. Plug in the known values into the logistic growth model equation:
64 million = K / (1 + A * e^(-0.053 * t))
3. Since we don't have information about the initial population size (A) or the specific time (t), we can simplify the equation as follows:
64 million = K / (1 + 0 * e^(-0.053 * t))
64 million = K
Therefore, the country's carrying capacity is 64 million.