Question

number of bacteria in a certain population Increases according to a continuous exponential growth model with How many hours does it take the size of the sample to double ? growth rato parameter of 48% per hour

Answer 1

It takes 1.77 hours for the population to double.

Explanation:

Equation for population growth:

The equation for population growth, after t hours, with a growth rate parameter of r, as a decimal, is given by:

`P(t) = P(0)(1+r)^t`

Growth rato parameter of 48% per hour

This means that
`r = 0.48`. So

`P(t) = P(0)(1+r)^t`

`P(t) = P(0)(1+0.48)^t`

`P(t) = P(0)(1.48)^t`

How many hours does it take the size of the sample to double?

This is t for which P(t) = 2P(0). So

`P(t) = P(0)(1.48)^t`

`2P(0) = P(0)(1.48)^t`

`(1.48)^t = 2`

`\log{(1.48)^t} = \log{2}`

`t\log{1.48} = \log{2}`

`t = \frac{\log{2}}{\log{1.48}}`

`t = 1.77`

It takes 1.77 hours for the population to double.