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

1 answer

To determine the population of the bacteria after 516 minutes, we first need to calculate how many doubling periods fit into that time frame.

  1. Find the number of doubling periods: \[ \text{Number of doublings} = \frac{\text{Total time}}{\text{Doubling time}} = \frac{516 \text{ minutes}}{129 \text{ minutes}} = 4 \]

  2. Since the population doubles every doubling period, we can calculate the population after 4 doublings using the formula: \[ \text{New population} = \text{Initial population} \times 2^{\text{Number of doublings}} \] Plugging in the values: \[ \text{New population} = 10,710 \times 2^4 \]

  3. Calculate \(2^4\): \[ 2^4 = 16 \]

  4. Now multiply the initial population by the growth factor: \[ \text{New population} = 10,710 \times 16 = 171,360 \]

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