Sign up ×
Mathematics Stack Exchange is a question and answer site for people studying math at any level and professionals in related fields. It's 100% free, no registration required.

In the exponential growth formula, $N = N(0)e^{kt}$, I know that $t$ is for time, but what is the unit of measure? Years? Months? Days? Hours?

share|cite|improve this question
Depends on the problem, but generally $t$ is dimensionless in the general formula: $N = N_0e^{kt}$. – William Feb 15 '12 at 20:49
Inside the exponential, that should be dimensionless. So if you want $t$ to be in sec, then $k$ should be in 1/sec. – GEdgar Feb 15 '12 at 21:07

1 Answer 1

$$\frac{dN}{dt} = kN$$ That is, the rate of the growth of the population is directly proportional to the number at that instant.

The units of k will determine the units for t.

When solved for N, $$\frac{dN}{N} = k.dt$$ $$\int_{N_0}^N\frac{dN}{N} = \int_0^t k.dt$$ $$\ln \frac{N}{N_0} = kt$$ $$N = N_0.e^{kt}$$

share|cite|improve this answer

Your Answer


By posting your answer, you agree to the privacy policy and terms of service.

Not the answer you're looking for? Browse other questions tagged or ask your own question.