Graph Exponential Growth Functions

Lesson 7.1Algebra II

Strauss

Agenda

1. Tests will be returned on Wed/Thursday. If you wish to see it beforehand you may come in at lunch or 7th period.

2. New assignment sheets and seats.3. Lesson 7.1 Graph Exponential Growth

Functions4. Homework: Lesson 7.1 from the assignment

sheet.

Lesson 7.1 Graph Exponential Growth Functions

Here is an old riddle:

You have the choice of receiving $1000/day for 20 days or you can start with $1 and have it doubled every day for the next 20 days. Which should you choose and why? Work on that!

Lesson 7.1 Graph Exponential Growth Functions

The “winning” example on the previous page is exponential growth. Let’s see if we can come up with an equation to determine how much money you would have at any time during the process.

Lesson 7.1 Graph Exponential Growth Functions

The equation that you came up with should look something like this:

This is an exponential growth function.. The general form is . Identify for the equation above.

Lesson 7.1 Graph Exponential Growth Functions

Now let’s graph the equation. What would the domain be for the problem? We are going to ignore the domain for a little to see the general graph of an exponential equation.

Make a t-chart choosing both positive and negative integers for What is the domain and what is the range of this equation?

Lesson 7.1 Graph Exponential Growth Functions

Ok, let’s change to 3 and see what happens. State the domain and range.

Let’s make a -1 and see what happens. State the domain and the range.

Let’s go back to as your parent function. Come up with an equation to move it 4 units to the right and 3 units down. State the domain and the range.

Lesson 7.1 Graph Exponential Growth Functions

In the old days…. say 20 years ago, saving accounts were very popular. One could earn interest on their money in the bank… here’s how it worked.

You would make a deposit called the principal. The bank would pay you interest on the money that you had in the account. The bank would take into consideration how much was in the account after the interest was applied and then pay you interest on the new amount. This is called compounding.

Lesson 7.1 Graph Exponential Growth Functions

Let’s say that you had $1000 and (the old days) you were able to find a bank that gave 5% interest per year, compounded monthly. Could you figure out how much money you would have with 1 months worth of interest? How about 2 months? How about a year.

How did you figure it out?

Lesson 7.1 Graph Exponential Growth Functions

If you did this correctly you should be able to get your process into one formula, given by: Where:

And