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

Answer 1

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.