Final answer:
The population increase is fastest when the rate of growth is highest in the Gompertz equation.
Step-by-step explanation:
The fastest population increase for the Gompertz equation occurs when the rate of growth is at its highest. In the context of the Gompertz equation, the rate of growth is represented by the difference between the initial rate (r₁) and the final rate (r₂). The population increase can be calculated using the formula e^(r₁ - r₂), where e is the base of the natural logarithm.
For example, if the initial rate is 1 Gppl and the final rate is 8 Gppl, we can compute the population increase as follows:
In(8/1)/In 1.01 = 13.4
Therefore, the population would increase from 1 Gppl to 8 Gppl in approximately 13.4 years at a growth rate of 1%.