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 of fall, the harbor has 150,000 square feet of algae. Suppose half of algae dies per month. Create a table and graph to repersent the relationship.​

Answer 1

The relationship between time and algae coverage in Green Top Lake can be modeled by the formula A(t) = 150,000 * (1/2)^t, where A is the amount of algae in square feet, and t is the time in months. A table and graph of this data would show an exponential decay, with algae coverage halving every month from an initial amount of 150,000 square feet at the beginning of fall.

Step-by-step explanation:

To represent the relationship between time and the amount of algae in the harbor at Green Top Lake as the weather gets colder, we'll assume that half of the algae dies each month starting from an initial coverage of 150,000 square feet at the beginning of fall.

Algae Coverage Over Time

Let's define the following variables:

A for the amount of algae in square feet.

t for time in months from the start of fall.

We know that the algae halves every month, so the amount of algae at time t can be calculated using the formula A(t) = 150,000 * (1/2)^t, where A(0) = 150,000.

Table of Algae Coverage

Month 0 (start of fall): 150,000 sq ft

Month 1: 75,000 sq ft

Month 2: 37,500 sq ft

Month 3: 18,750 sq ft

Month 4: 9,375 sq ft

Month 5: 4,687.5 sq ft

... and so on, halving each month.

This relationship can also be visualized on a graph with time on the x-axis and the algae coverage on the y-axis. The graph would show an exponential decay as the amount of algae decreases over time as shown in the attached picture.