Algebra Worksheets

Practice and master algebra concepts with our helpful walkthroughs and downloadable practice worksheets from our team of elite math educators.

Exponential Graphs

By Tina Goosz

An exponential graph is the graph of a function that represents the exponential properties of the function. An exponential function is a function where the variable appears as the exponent. The formula of this is y=bx. These are the inverse functions of logarithms.

Why is this concept useful?

Exponential functions have multiple scientific uses, including population growth, virus reproduction, and radioactive decay. These problems can also be seen in finance in regards to credit cards, bank accounts, and loans.

Where does this concept fit into the curriculum?

High School

How can we use the concept:

Formula: y=bx where b > 0Formula:\ y=b^{x} \ where\ b\ >\ 0

If b is greater than 1, the function will increase exponential by b. This is exponential growth.

If b is less than 1, the function will decrease exponentially by b. This is exponential decay.

Let us consider

y=3xy=3^{x}

We will choose values for x and substitute these into the equation to generate values for y.




Sample Math Problems

1. Let us consider

y=6xy=6^{x}

Solution:

We will choose values for x and substitute these into the equation to generate values for y.


2. Let us consider

y=4.5xy=4.5^{x}

Solution:
We will choose values for x and substitute these into the equation to generate values for y.

3. Let us consider

y=(12)xy=(\frac{1}{2})^{x}

Solution:
We will choose values for x and substitute these into the equation to generate values for y.

Notice that with a b value less than one, the graph has inverted directions.

4. Let us consider

y=(56)xy=\left(\frac{5}{6}\right)^{x}

Solution:
We will choose values for x and substitute these into the equation to generate values for y.

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As a parent, you hope your child is extremely successful and likely become the next Gates, Zuckerberg, or Meg Whitman. To set your child on the right path, there are many skills and traits that you can start building and nurturing now. Doing so plants the seeds for future success.

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Practice Math Problems

1. Draw the graph for the following function:

y=4xy=4^{x}

2. Draw the graph for the following function:

y=5.5xy=5.5^{x}

3. Draw the graph for the following function:

y=13xy=\frac{1}{3} x

4. Draw the graph for the following function:

y=34xy=\frac{3}{4} x

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