Context 17 - Big Fish Story

As a class, we have defined equilibrium as...

Determine how many fish are in the pond initially.

What are some reasons that the fish population would decrease in this pond? Share your ideas below.

What are some naturally occurring reasons that the fish population would increase in this pond? Share your ideas below.

What is the overall rate of change for the fish population of this pond?

Write a NEXT-NOW formula (also known as a recursive formula) to describe what is happening with the fish population in the pond over time. [An example of a NEXT-NOW formula is that if something is growing by 10% each year, the formula would be: NEXT = 1.1(NOW)]

Grandpa wanted to stock this pond, but only has a budget of $150. The prices from Dunn’s Fish Farm in Oklahoma are below. Determine how many fish you would recommend that Grandpa should buy.

Write a NEXT-NOW statement to include the overall rate of change and the restocking number that you determined for the fish population in this pond.

Use a spreadsheet to examine the change in the fish population

Here's a sample spreadsheet

Make a visual representation using technology. Screenshot the result and paste it below.

How many years does it take for your population to reach “equilibrium”?

What is the value of the population at “equilibrium”?

What if your grandpa’s budget were raised to $300? How would that change the number of fish to be restocked annually?

What is a recursive formula and how does it work?

Why is a linear model not appropriate for this model?

What is equilibrium?