Question

A certain number of bacteria are in a petri dish. If the growth rate is 2.7 percent per hour, how many hours will it take the bacteria to double in number?

Answer 1

Using the rule of 70, which states that the doubling time in hours is equal to 70 divided by the growth rate percentage, it will take approximately 25.93 hours for the bacteria to double in number at a growth rate of 2.7 percent per hour.

Step-by-step explanation:

To calculate the time it will take for the bacteria to double in number with a growth rate of 2.7 percent per hour, we can use the rule of 70. The rule of 70 states that we can find the doubling time by dividing 70 by the percentage growth rate.

Doubling time = 70 ÷ growth rate percentage = 70 ÷ 2.7 ≈ 25.93

Therefore, it will take approximately 25.93 hours for the bacteria to double in number.

Answer 2

time = log (end amount) -log (bgng amt) / log (1 + rate)
If we're waiting for it to double, then we'll say beginning amount = 100 and ending amount = 200.
time = [log (200) -log (100)] / log (1.027)
time = 2.3010299957 - 2 / 0.011570443597
time = .3010299957 / 0.011570443597
time = 26.0171525125 hours