Exponential+Functions-Target+C-Growth+Rates-Guided+Learning

Target C - Determine if a table represents an exponential or linear function. If it is an exponential, determine the growth rate.

 * [[image:Discuss this.png width="173" height="97"]] || Keon and Serena have to choose between two different discount options at an electronics store, 30% off or 15% off followed by another 15% off. Serena thinks that the 30% off is the better option. Keon disagrees and thinks that both discounts are equal. Whom do you agree with and why? ||

As we continue our discussion of exponential functions, it will be helpful to determine if a set of data is linear, exponential or possibly modeled by some other function. We could graph each set of data and look at the graph to determine if a line or exponential would best fit the data. Or as we learned in the Linear Functions unit, a function is considered linear when it's slope is constant or we have a common difference between //x// and //y// values. We can determine this using the table and some subtraction. How can we determine if a function is exponential? Let's look at a set of data that is exponential and see if we can determine why it is exponential.

The table below is the function //y// = 3// x //. What we notice is in order to get the next //y// value you multiply the previous //y// value by 3. The table below represents the function //y// = 2. 2// x //. What we notice is to get the next y value you are multiplying the previous by 2.

The table below represents the function //y// = 0.5 // x //. What we notice about the y-values in this final table is you need to multiply by 0.5 to get to the next //y//-value.



Now we can see a function is considered exponential if you are multiplying by a constant number to get to the next value in the table or you have what is called a common ratio.

So now we know how to determine if a function is linear or if it is exponential. Let's look at the video below to see a few more examples.

media type="youtube" key="x36yjjdtGjM" width="560" height="315"

Now that we can determine if a data set represents a linear or exponential function, let's see how to determine the growth rate if the function is exponential. Looking at our first table (below), once we know that it is exponential, in order to determine the growth rate we need to divide the a //y//-value by the previous //y//-value and this will give us the growth rate.




 * Quick Check - Exponential Functions - Target C - Growth Rates **

Determine if the following sets of data are linear or exponential. If they are exponential determine the growth rate.

a)

b)

Quick Check Solutions - Exponential Functions - Target C - Growth Rates