A certain type of bacteria is growing at an exponential rate that is modeled by the equation y= ae^kt, where t represents the number of hours. There are 100 bacteria initially, and 500 bacteria five hours later.

The number of bacteria after t hours is given by:

Step-by-step explanation:

Amount of bacteria after t hours:

Is given by the following equation:

In which a is the initial value and k is the constant of growth.

There are 100 bacteria initially

This means that . So

500 bacteria five hours later.

This means that . We use this to find k. So

So

The number of bacteria after t hours is given by:

7

step-by-step explanation: