This section explores how changes in b affect the exponential equation y = ab^x.

Exponential Equations

y = ab^x

Both exponential growth and exponential decay use the same equation, changes in the variable affect the graph of the function.

1. Follow the link below.
2. On the left, make sure c = 0 and a = 1.
3. Move b.

Exponential Equations

This is a screenshot of the applet.

Source: Analyze Math, Exponential Functions

Example: Create an exponential function that has a y-intercept of 1 and where the y-values double for each x-value.

Answer the following in your notes.

Click on the blanks to reveal the answers.

• The exponential equation is Interactive button. Assistance may be required. ____ y = 2^x , the y – value at x = 1 is Interactive button. Assistance may be required. ____ 2 .
• On the left, change the b to 3, the new equation is Interactive button. Assistance may be required. ____ y = 3^x the y-value at x = 1 is Interactive button. Assistance may be required. ____ 3.
• Change b to 4, the new equation is Interactive button. Assistance may be required. ____ y= 4^x the y – value at x = 1 is Interactive button. Assistance may be required. ____ 4.
• The graph Interactive button. Assistance may be required. ____ increases faster as the base increases.
• Change b to 2, the new equation is Interactive button. Assistance may be required. ____ y= 2^x y – value x = 1 at is Interactive button. Assistance may be required. ____ 2.
• Change b to 0.5, the new equation is Interactive button. Assistance may be required. ____ y= 0.5^x y – value at x = 1 is Interactive button. Assistance may be required. ____ 0.5.
• When the b – value, or base, moves from 2 to 0.5, the graph changed from an exponential growth function to an Interactive button. Assistance may be required. ____ exponential decay function, the base (b) is Interactive button. Assistance may be required. ____ less than 1.