Question

A colony of 10,710 bacteria doubles in size every 129 minutes. What will the population be 516 minutes from now?
bacteria

Answer 1

To find the population of the bacteria colony after 516 minutes, we can use the formula for population growth due to doubling:

\[
P = P_0 \times 2^{t/T}
\]

Where:
- \(P\) is the future population
- \(P_0\) is the initial population (10,710)
- \(t\) is the total time elapsed (516 minutes)
- \(T\) is the time it takes for the population to double (129 minutes)

First, we calculate how many doubling periods fit into 516 minutes:

\[
\text{Number of doublings} = \frac{t}{T} = \frac{516 \text{ minutes}}{129 \text{ minutes}} = 4
\]

Now, we can calculate the population after 4 doublings:

\[
P = 10,710 \times 2^4
\]

Calculating \(2^4\):

\[
2^4 = 16
\]

Now, plug this back into the equation:

\[
P = 10,710 \times 16 = 171,360
\]

Thus, the population of the bacteria colony after 516 minutes will be:

\[
\text{Population} = 171,360
\]

So, the final answer is:

**171,360 bacteria**.