6.3 Graphing Exponential Functions

Predicting the graph

Use the data table to answer the questions.

DESMOS: Marbleslides: Exponentials

An exponential function has the general form y = abx +c Manipulating these variables will alter the function graph. Follow your teacher’s instructions to complete this exploratory Desmos activity. Then, answer the summary questions.

5-Point Practice: Writing an Exponential Equation From a Table

Complete any number of problems that add up to 5 points. Identify how the graph behaves when x is very large and when x is very small: does it approach ∞, -∞, or a specific value. Then give the equation of the asymptote.

Level 1

Jerry bought a brand new car at the dealership one year ago for $35,000. The value of his car depreciates and is worth 20% less every year.

Level 2:

Although the prices of stocks and bonds fluctuate constantly, you can model the growth by using an exponential function that approximates the growth as if it were the same year after year. This growth is called the annualized rate of return, and you can use it as the base in an exponential function model.

Let’s say Jenny and Sarah are both gifted $5,000 when they were born and they are 16 years old now. Jenny’s money is invested in an S&P Index Fund with 7.5% average annualized returns while Sarah’s is invested in a bond fund with 3.5% average annualized returns.

The Power of Time

Shandra took a finance class in high school , and her twin brother Abdul did not. So when they both started working full-time jobs at the age of 25, Shandra invested in a retirement account right away. She put in $5,000 the first year in an account that has an average annual rate of return of 6%. Abdul waited 5 years until he was 30 before doing the same. In reality, they would both continue investing, but we will look at the growth of just this FIRST $5,000.