Notice that the logistic equation looks like the exponential equation multiplied by [1-(N/K)]. This mathematical term is what accounts for the density-dependent population growth rate.

Lake divided into 50 equally sized squares with each square that can only support one fish on average.

   

Number of Fish (N)	[1-(N/K)]
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Notice that the logistic equation looks like the exponential equation multiplied by [1-(N/K)]. This mathematical term is what accounts for the density-dependent population growth rate.

This gives the per capita growth rate of the population, which is represented as:

The per capita growth rate is mathematically interchangeable with the variable r (realized intrinsic rate of increase). r is the rate of increase at each moment in time. Therefore:

Given this equation for r:

Predict what happens to r as the population reaches K.

If K = 50 and r_max = 0.5, when will r be exactly half of r _max?

r will be exactly half of r_max when N equals:

Number of Fish (N)