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?

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Answer 1 · 2017-03-30T18:08:06

51.73 minutes.

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

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

Dividing these equations

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

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

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)N=42e^(0.0134t). How long will it be before the population bacteria doubles?