Question

A microbiologist determines that a colony of bacteria doubles every hour. If at the start (t = 0) there are 10 in the colony,

a) What is the population at the end of 1 day?

Answer 1

The population at the end of 1 day is 2^24 ×10, as the bacteria doubles every hour over 24 hours.

In a situation where a colony of bacteria doubles every hour, the population at any given time can be modeled by an exponential growth function. The general form of such a function is P(t)=P0​×2^(t/h), where P(t) is the population at time t, P0​ is the initial population, h is the doubling time, and t is the elapsed time.

In this case, at the start (t=0), the initial population (P0 ) is given as 10, and the doubling time (h) is 1 hour since the colony doubles every hour. Therefore, the specific exponential function for this scenario is P(t)=10×2^t/1.

To find the population at the end of 1 day (24 hours), substitute t=24 into the function:

P(24)=10×2^24/1=10×2^24≈167772160.

So, the population at the end of 1 day is approximately 2^24 ×10, resulting from the continuous doubling of the bacteria population over the 24-hour period.