Learning Objectives:

__Math Tutoring on Graphing Exponential Functions__

An **Exponential Function** is a **function** in the form: **f (x) = abᵡ**, where **‘a’ **can't be equal to zero, **‘b’** must be greater than zero and ‘b’ can't be equal to one. If **‘a’** was equal to zero or **‘b’** was equal to one, we would have a **Constant Function**, not an **exponential function**. The value of **‘a’ **is called the **Initial Value** or **Starting Value** which is the **function** value when the input **‘x’** is equal to zero and therefore **‘a’** also gives us the **Vertical Intercept** which would be the ordered pair, **( 0, a).**The base **‘b’** is called the **Growth Factor** or **Decay Factor. **

**b = 1 + r**, where** r** is equal to the growth rate per unit of time as a decimal. So if the base **‘b’** is greater than one, then **‘r’**, the growth rate, would have to be greater than zero or positive, and therefore the **function **represents **exponential growth** which is the **function** increasing at a constant percentage with a growth rate of **‘r’**. Now if the base **‘b’** is between zero and one, that means **‘r’** the growth rate would be negative, or less than zero, and therefore the **function** represents **exponential decay** which is the **function** decreasing at a constant percentage and the decay rate is equal to the opposite value of **‘r’**.

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**Hook Questions**** **

*1. **What is an Exponential Function?*

*2. **What is known as Initial Value?*

*3. **What is Growth Factor?*

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