Question

In a lab experiment, 260 bacteria are placed in a petri dish. The conditions are such

that the number of bacteria is able to double every 26 hours. How long would it be, to
the nearest tenth of an hour, until there are 350 bacteria present?

Answer 1

To find out how long it would take for the number of bacteria to reach 350, we need to determine how many times the bacteria will double in that period. Since the bacteria double every 26 hours, we can calculate the number of doubling times by taking the logarithm base 2 of the target number and dividing it by the rate of doubling. Using this calculation, we find that it would take approximately 19.5 minutes for the number of bacteria to reach 350.

Step-by-step explanation:

To find out how long it would take for the number of bacteria to reach 350, we need to determine how many times the bacteria will double in that period.

Since the bacteria double every 26 hours, we can calculate the number of doubling times:

1. Take the logarithm base 2 of the target number (350): log2(350)
2. Divide the result by the rate of doubling (26 hours): log2(350) / 26

Using a calculator, we find that log2(350) ≈ 8.45. Dividing this by 26 gives us approximately 0.325. Therefore, it would take approximately 0.325 hours, or 19.5 minutes, for the number of bacteria to reach 350.