Sample Problem - If Imax is 0.75 and the carrying capacity of the environment is 800, calculate
the growth rate for the following values for N: 100, 200, 400, 600, 700, and 800
To calculate the growth rate, we can use the formula:
Growth rate (r) = (Imax - N / K) * 100
where:
Imax = maximum intrinsic growth rate
N = current population size
K = carrying capacity of the environment
Let's calculate the growth rate for each value of N:
For N = 100:
r = (0.75 - 100 / 800) * 100
r = (0.75 - 0.125) * 100
r = 0.625 * 100
r = 62.5%
For N = 200:
r = (0.75 - 200 / 800) * 100
r = (0.75 - 0.25) * 100
r = 0.5 * 100
r = 50%
For N = 400:
r = (0.75 - 400 / 800) * 100
r = (0.75 - 0.5) * 100
r = 0.25 * 100
r = 25%
For N = 600:
r = (0.75 - 600 / 800) * 100
r = (0.75 - 0.75) * 100
r = 0 * 100
r = 0%
For N = 700:
r = (0.75 - 700 / 800) * 100
r = (0.75 - 0.875) * 100
r = -0.125 * 100
r = -12.5%
For N = 800:
r = (0.75 - 800 / 800) * 100
r = (0.75 - 1) * 100
r = -0.25 * 100
r = -25%
Therefore, the growth rates for the given values of N are as follows:
100: 62.5%
200: 50%
400: 25%
600: 0%
700: -12.5%
800: -25%