The formula for an increasing population is given by P(t) = P0 ert where P0 is the initial...

The formula for an increasing population is given by P(t) = P0 ert where P0 is the initial population and r > 0. Derive a general formula for the time t it takes for the population to increase by a factor of M.

Expert Solution

Consider that the formula for an increasing population is given by P(t) = P0ert, where P0 is the initial population and r > 0.

Put P(t) = MP0

Hence,

MP0 = P0ert

ert = M

rt = ln(M)

t = ln(M)/r

Hence, the general formula for the time t it takes for the population to increase by a factor of M is given by t = ln(M)/r.

Umair answered 1 year ago

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