In this unit, your student is introduced to exponential relationships. Earlier, your student studied what mathematicians call linear relationships, where they start with a quantity and add or subtract the same amount repeatedly. In an exponential relationship, they start with a quantity and multiply by the same amount repeatedly.

Exponential relationships are represented by equations in the form , where is the quantity you start with, is the growth factor that you are going to multiply it by, and is how many times you are going to multiply by . If is bigger than 1, the amount is growing, and if is less than 1, the amount is shrinking. When is equal to 1, the amount is staying the same.

Here is a task to try with your student: 

Florida is having a problem with a toxic green algae that is floating on their waterways, contaminating the water and killing the marine life. Kiran lives on a small lake in south Florida. One day he noticed 3 square meters of algae floating on the lake. A month later, the algae had doubled in size, growing to 6 square meters.

1. If the doubling pattern continues, how many square meters of the lake will be covered in algae in 4 months?
2. If the surface area of the lake is about 1,500 square meters, after how many months will the entire lake be covered?

Solution: 1. This can be solved using a variety of strategies. You could use a table, an equation, or a graph.