Question

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

Answer 1

Step-by-step explanation:

Continuous exponential growth model:

$population = population(t = 0) \times e ^{ \alpha t}$

Where α is the growth rate parameter.

So if t is the starting point and t+t1 is the point that population is doubled:

$\frac{population(t + t1)}{population(t)} = \frac{2 \times population(t)}{population(t)} = 2 = {e}^{ \alpha \times t1 }$

So:

$ln(2) = \alpha \times t1$

And as a result, t1, the time needed for the population to double at ANY given point is equal to:

$t1 = \frac{ ln(2) }{ \alpha }$