Question

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

Answer 1

To find the population of the bacteria after 516 minutes, we can follow these steps:

1. **Determine how many doubling periods fit into 516 minutes.**
\[
\text{Number of doublings} = \frac{516 \text{ minutes}}{129 \text{ minutes per doubling}} = 4
\]

2. **Calculate the population after the number of doublings.**
The formula for population growth through doubling is:
\[
P = P_0 \times 2^n
\]
where:
- \( P_0 \) is the initial population (10,710),
- \( n \) is the number of doublings (4).

Plugging in the values:
\[
P = 10,710 \times 2^4
\]
\[
P = 10,710 \times 16
\]
\[
P = 171,360
\]

Thus, the population of the bacteria after 516 minutes will be **171,360**.