# Exponential Function Worksheets

Exponential functions are those the type that include the use of exponents to some degree. They follow the form f (x) = c^{x}, where (x) represents the variable and (c) serves as the base. The consist of a constant as their base and variables serve as their exponent. If you find a situation where the variable serves as the base and the constant as the exponent this would be reclassified as a power function. These types of functions are really helpful for evaluating exponential growth or decay. You will find this used in many financial transactions and scientific population studies. These worksheets help students learn how to write exponential functions as an expression. You will also learn how to evaluate word problems that in involve their use.

### Aligned Standard: HSF-IF.C.8b

- 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.

- Answer Keys - These are for all the unlocked materials above.

### 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?

### 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 is a constant and x is a variable, also b > 0 and b ≠ 1.

Let us consider an example where the exponential function is used to express the growth of the bacteria over time. Some bacteria become double after every hour. If you start with one bacterium and it becomes doubled 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

You will find the concept of exponential growth starts with a quantity slowly increasing in the beginning and then rapidly growing. When you graph this type of growth it represents a hockey stick pointed upward. Exponential decay inverts this concept, the quantity will rapidly decay at first and then slowly peel off. When you graph this, it is a hockey stick pointed downwards.