A culture of 100 bacteria grows at a continuous rate of 20%. Two hours later. 60 of the same type of bacteria are placed in a culture that allows a 30% growth rate. After how many hours do both cultures have the same population? Explain your answer.

Both cultures will have the same population after 11 hours.

Step-by-step explanation:

Exponential equation for population growth:

The exponential equation for population growth is given by:

In which P(0) is the initial population and r is the growth rate, as a decimal.

A culture of 100 bacteria grows at a continuous rate of 20%.

This means that . So

The other culture starts to hours later, and we want to take that time as a parameter. So

Which means that when culture 2 growth starts, the population size of culture 1 is described by the following equation:

Two hours later 60 of the same type of bacteria are placed in a culture that allows a 30% growth rate.

This means that . So

After how many hours do both cultures have the same population?

This is t for which:

So

Both cultures will have the same population after 11 hours.