You need to integrate then evaluate. THat is fundamental theorem.

I think it is the chain rule.The size of bacteria population depends on the availability of the nutrients as food. The rate at which the bacteria population is changing with time is the product of the rate at which availability of nutrients changes with time and the rate at which the bacteria population changes in reaction to the change in the nutrient availability

The theorem is ___________

Because the differencial equation is,

For some constant.

Divide by *)

Integrate and use the chain rule.

*)It is nowhere zero because we assume the population always exists.