Question

The harbor at Green Top Lake has a lot of green algae at the end of the summer. However, as the weather gets colder, the algae begins to die. At the beginning, the harbor has 150,000 square feet of algae. Half of the algae dies each month. Fill in the table to describe the relationship. Is the relationship linear or exponential? Write a function to describe the relationship.

Answer 1

The relationship between the algae cover and time at Green Top Lake is exponential decay, represented by the function A(n) = 150,000 × (1/2)^n, where A(n) is the area of algae after n months.

Step-by-step explanation:

The relationship between the amount of algae in the harbor at Green Top Lake and time is an exponential decay because it is described by a quantity decreasing by a consistent percentage over regular intervals. Given the initial amount of 150,000 square feet of algae, we can fill in the table showing that the algae cover is halved each month. To write a function describing this relationship, let A(n) represent the area covered by algae after n months:

A(n) = 150,000 × (½)^n

Where A(n) is the algae area in square feet and n is the number of months passed. This function shows that for each month n, you multiply the original amount by 1/2 raised to the power of n, which accurately represents the halving process that happens each month.

As an example, after 2 months, the area covered by algae would be:

A(2) = 150,000 × (½)^2 = 150,000 × 1/4 = 37,500 square feet.