Question

There is a population of 405,000 bacteria in a colony. If the number of bacteria doubles every 44 hours, what will the population be 176 hours from now?

Answer 1

Since the population doubles every 44 hours, it can be modeled using an exponential equation as follows:

$P(t)=405,000\times2^{\frac{t}{44}}$

Where t is the time since the population was 405,000 measured in hours.

Replace t=176 to find the population after 176 hours:

$\begin{gathered} P(176)=405,000\times2^{\frac{176}{44}} \\ =405,000\times2^4 \\ =405,000\times16 \\ =6,480,000 \end{gathered}$

Therefore, the population after 176 hours will be 6,480,000