Question

The number of bacteria in a certain population increases according to a continuous exponential growth model, with a growth rate parameter of
6.1%
per hour. How many hours does it take for the size of the sample to double?..............

Note: This is a continuous exponential growth model.
Do not round any intermediate computations, and round your answer to the nearest hundredth.

Answer 1

Let N be the number of bacteria as function of the time in hours, and let No be the initial number of bacteria.
\[\large N=N _{0}e ^{0.061t}\]
\[\large \frac{N}{N _{0}}=2=e ^{0.061t}\]
\[\large 0.061t=\ln 2\]
\[\large t=\frac{\ln 2}{0.061}=you\ can\ calculate\]