Determine whether each equation demonstrates exponential growth or decay. Find the rate of increase or decrease for each. 1. y=7^x 2. y=2(8)^x 3. y=0.9(.2)^x

Question

My teacher is out sick and we have a substitute that isn't the best at teaching math. I don't want to fail my quiz due to a lack of resources. 

Answer 1

Hi Breanna,

 

If you're looking at an exponential function with the form:

 

     y = ca^x

 

Just look at the value of a, the number that's being raised to the power of x.

 

If |a| > 1, then you're looking at exponential growth.

 

If |a| < 1, then you're looking at exponential decay.

 

It's important to make sure that the sign in front of the x is positive. If it's negative, as in this example:

 

     y = 2(13)^-x

 

Then change it to a positive using what you know about exponents:

 

     y = 2(13)^-1x

     y = 2(1/13)^x

 

Hope this has helped! :)

Answer 2

exponential growth will have a base > 1
exponential decay will have a base < 1
1. y = 7^x
7 > 1
exponential growth, starts at 1 and increases by a rate of 7 for each unit of time x
3. y = 0.9(0.2)^x
0.2 < 1
exponential decay, starts at 0.9 and decreases at a rate of 0.2 for each unit of time x