Question

A population of bacteria doubles every 15 hours. Initially, the population of bacteria
is 50.
What is the population of the bacteria after 40 hours?
Enter your answer, rounded to the nearest whole number, in the box.

Answer 1

Answer:

About 317 bacteria.

Step-by-step explanation:

We can use the model for exponential growth:

$\displaystyle f(t) = ar^{t/d}$

Where t is the time (in hours) that has passed and d is the time in which one "cycle" occurs.

Since the initial population is 50 bacteria, a = 50:

$\displaystyle f(t) = 50r^{t/d}$

The population doubles every 15 hours. Hence, r = 2 and d = 15:

$\displaystyle f(t) = 50(2)^{t/15}$

Therefore, the population after 40 hours will be:

$\displaystyle \begin{aligned} f(40) & = 50(2)^{(40)/15} \\ \\ & =50(2)^{8/3} \\ \\ & = 317.48 \approx 317 \end{aligned}$

In conclusion, the population of the bacteria after 40 hours will be about 317 bacteria.