Question

A population of bacteria is growing in such a way a that the number of bacteria present, N, after t minutes is given by the rule `N=42e^(0.0134t)`. How long will it be before the population bacteria doubles?

Answer 1

51.73 minutes.

Explanation:

1. Let the population be `N` at `t=t_1`.
2. Let the population be twice i.e. `2*N` at `t=t_2`.

`therefore delta t = t_2-t_1` where `delta t` is the time required for population to double.

`therefore` we obtain two equations from above conditions:-

1. `N = 42*e^(0.0134*t_1)`
2. `2*N = 42*e^(0.0134*t_2)`

Dividing these equations

`2 = e^(0.0134*(t_2-t_1)) = e^(0.0134*delta t)`

Taking natural logarithm on both sides;
`ln(2) = 0.0134 * delta t`
`implies` `delta t = 51.73`