A population of bacteria is growing at the rate of 2.3% per minute.

Question

6. A population of bacteria is growing at the rate of 2.3% per minute. Calculate how long it will take for the size of the population to double. Give your answer to the nearest minute.

Answer 1

A growth rate of 2.3% per minute means that at the end of each minute, the population is 1.023 times what it was at the start of the minute.

 

P(t) = P(0) (1.023)^t, t in minutes.

 

Doubling time:

 

2P(0) = P(0) (1.023)^T

 

2 = (1.023)^T

 

T = log2/log1.023 minutes ≅ 30.48 minutes