Question

Otter Lake is a town that has an estimated yearly population increase of 10% each year. Today the populations stands at 15 thousand people.

Please provide the following in your answer with all work show for credit:
- Write an equation to represent the population increase
- A data table to demonstrate the increase with a minimum of 5 data points.
- Draw a hand drawn graph of the population function
- Determine what the population will be in ten years from today.

Write a detailed explanation to the questions below:
1. How does the graph of this Exponential function behave?
2. How do asymptotes of Exponential functions play a role in this specific example?
3. How do the limits of an Exponential function play a role in this specific example?

Answer 1

You have a lot of questions here, I will be happy to help with the first couple of questions.

This example is an exponential equation situation. The equation is in the form of y = ab^x. Where a is the starting amount, b is the rate and x is the number of years.

Therefore, our equation would be: y = 15000(1.1)^x

To make your chart, just plug in the number of years for x and evaluate.