A tumor may be regarded as a population of multiplying cells. It is found empirically that...

A tumor may be regarded as a population of multiplying cells. It is found empirically that the “birth rate” of the cells in a tumor decreases exponentially with time, so that β(t) = β0e−αt (where α and β0 are positive constants), and hence

Solve this initial value problem for

Observe that P(t) approaches the finite limiting population P0 exp (β0/α) as t→ + ∞