Question

A culture of bacteria has an initial population of 22000 bacteria and doubles every 5 hours. Using the formula P t = P 0 ⋅ 2 t d P t ​ =P 0 ​ ⋅2 d t ​ , where P t P t ​ is the population after t hours, P 0 P 0 ​ is the initial population, t is the time in hours and d is the doubling time, what is the population of bacteria in the culture after 17 hours, to the nearest whole number?

Answer 1

We have been given that a culture of bacteria has an initial population of 22,000 bacteria and doubles every 5 hours. Using the formula $P(t) = P_0\cdot 2^{\frac{t}{d}}$, where P(t) ​ is the population after t hours, ​$P_0$ is the initial population, t is the time in hours and d is the doubling time.

We are asked to find the population of bacteria after 17 hours.

First of all, we will substitute our given values in doubling life formula as:

$P(t) =22,000\cdot 2^{\frac{t}{5}}$

Now to find population of bacteria after 17 hours, we will substitute $t=17$ in our formula as:

$P(117) =22,000\cdot 2^{\frac{17}{5}}$

$P(117) =22,000\cdot 2^{3.4}$

$P(117) =22,000\cdot (10.556063286183)$

$P(17) =232233.392296026$

$P(17)\approx 232,233$

Therefore, the bacteria population will be 232,233 after 17 hours.