NationalMediumFunctions10–12

Continuous Growth of a Bacterial Culture

Crescimento Contínuo de uma Cultura de Bactérias

A culture grows continuously according to $N(t) = N_{0}e^{kt}$ , where $t$ is measured in hours. At $t = 0$ there are $500$ bacteria and after $3$ hours there are $800$ . Find $k$ and predict the population after $10$ hours.

The known pair of values gives one equation in $k$ ; a logarithm is what releases an exponent. Keep $k$ exact until the final substitution.

Solution

Step 1 of 5

1.From $N(0) = 500$ we get $N_{0} = 500$ . Then