## Expressions for Exponential Functions

#### Aligned To Common Core Standard:

**High School Interpreting Functions** - HSF-IF.C.8b

How to Write Expressions for Exponential Functions?
Exponential expression is probably one of the essential functions in mathematics. We learned linear functions where the highest power of the variables is 1. Any equation constructed represents a line on the graph and a linear equation represents a straight line. However, it may not be the case every time, considering that there are curves as well. Such sequences have a non-linear equation to its name. One of those linear expressions is the exponential function. The exponential function has the form f(x)= b^{x}, where b > 0 and b ≠ 1.
Let us consider an example where the exponential function is the growth of the bacteria. Some bacteria become double after every hour. If you start with one bacterium and it becomes double after every hour, then you have 2n bacteria after n hours. We can write the function in the form of f(x)= 2^{x}. Let us place values for different values of x.
First Bacteria (x = 0), f(0)= 2^{0} = 1 | After 1 hour: f(1)= 2^{1} = 2
After 2 hours: f(2)= 2^{2} = 4 | After 3 hours: f(2)= 2^{3} = 8 | After 4 hours: f(2)= 2^{4} = 16 | After 5 hours: f(2)= 2^{5} = 32
These worksheets help students learn how to write exponential functions as an expression.

### Printable Worksheets And Lessons

- Sofia's Loan Step-by-step
Lesson- I have a feeling that Sofia doesn't have a lot of friends
at that interest rate.

- Guided Lesson
- William and Rosy are investing, while John is borrowing quite
a bit of change.

- Guided Lesson
Explanation - Everything is based on the compound interest formula.

- Practice Worksheet
- "So banks take your money and give it to other people? That's
not fair!" Straight from my grand daughters mouth.

- Matching Worksheet
- This is more of a word problem set than anything else.

#### Homework Sheets

The finance world makes a living off of this type of work.

- Homework 1 - Robert gives $1,400 to his brother at 8% interest rate per year. Robert's brother pays back the entire amount plus interest; after 2 years. What was the total amount that Robert received?
- Homework 2 - Jackson takes $3,000 at an interest rate of 4% per year; compounded semi-annually. How much money will he return after 4 years?
- Homework 3 - Mack invests $65,000 at an 11% interest rate per year; compounded quarterly. Find the total balance after 9 years.

#### Practice Worksheets

If you have a deep understanding of this skill, you should be able to negotiate a better mortgage for yourself.

- Practice 1 - Milton borrowed $22,000 at a 6% interest rate per year; compounded semi-annually. Calculate the amount the total he owed after 3 years.
- Practice 2 - George lends $4,500 at 7% interest rate per year; compounded semi-annually. How much money will he get back after 2 years?
- Practice 3 - Stephan borrowed $18,000 at 6% interest rate per year; compounded semi-annually. If he were to pay off the loan after 5 years, how much would he have paid in full?

#### Math Skill Quizzes

You will deal with some much larger numbers here.

- Quiz 1 - Mrs. Maria borrows $61,000 at a 7% interest rate per year compound semi-annually. Calculate the amount she will owe after 9 years.
- Quiz 2 - Jenifer saves $7,600 at a 5% interest rate per year; compounded semi-annually. How much money will she get back after 3 years?
- Quiz 3 - Davis takes $66,000 at an interest rate of 12% per year; compounded semi-annually. How much money will he return after 9 years?