Warm Up Solve: Simplify:

Review HW

Skills Check Pencil & calculator only When finished, flip it over, and sit quietly.

UNIT QUESTION: How can we use real-world situations to construct and compare linear and exponential models and solve problems? Standards: MCC9-12.A.REI.10, 11, F.IF.1-7, 9, F.BF.1-3, F.LE.1-3, 5 Essential Question: What is an exponential function and how is different from a linear function? What does their point of intersection represent?

Exponential Functions

First, let’s take a look at an exponential function y -2 1/4 -1 1/2 1 2 4

So our general form is simple enough. The general shape of our graph will be determined by the exponential variable. Which leads us to ask what role does the ‘a’ and the base ‘b’ play here. Let’s take a look.

First let’s change the base b to positive values What conclusion can we draw ?

Next, observe what happens when b assumes a value such that 0<b<1. Can you explain why this happens ?

will happen if ‘b’ is negative ? What do you think will happen if ‘b’ is negative ?

Don’t forget our definition ! Any equation of the form: Can you explain why ‘b’ is restricted from assuming negative values ?

To see what impact ‘a’ has on our graph we will fix the value of ‘b’ at 3. We are going to look at positive values of a today. What does a larger value of ‘a’ accomplish ?

Let’s see if you are correct ! Shall we speculate as to what happens when ‘a’ assumes negative values ? Let’s see if you are correct !

Our general exponential form is “b” is the base of the function and changes here will result in: When b>1, a steep increase in the value of ‘y’ as ‘x’ increases. When 0<b<1, a steep decrease in the value of ‘y’ as ‘x’ increases.

We also discovered that changes in “a” would change the y-intercept on its corresponding graph. Now let’s turn our attention to a useful property of exponential functions.

Linear, Exponential, or Neither

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 1. Linear

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 2. Exponential Rounds of Tennis 1 2 3 4 5 Number of Players left in Tournament 64 32 16 8

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 3. This function is decreasing at a constant rate. Linear

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 4. A person’s height as a function of a person’s age (from age 0 to100). Neither

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 5. Linear

For each representation of a function, decide if the function is linear, exponential, or neither. Give reasons for your answer. 6. Each term in a sequence is exactly 1/3 of the previous term. Exponential

Homework