# Exponential Functions Word Problems Worksheet with Answers

Exponential functions are one of the most applicable mathematics topics to the real-world. Whether it’s calculating compound interest or exploring the exponential decay of a radioactive substance, there are just so many real-world applications that make excellent exponential functions word problems! But since word problems can be tricky, I have put together an exponential functions word problems worksheet with answers to help!

Let’s get to the bottom of how to solve exponential functions word problems by exploring some real-world applications!

## What is an Exponential Function Word Problem?

Exponential growth and decay happen *everywhere *in the real-world. From the bacteria growing on your toilet seat to the compound interest you earn in you bank account, there are so many applications of exponential growth and decay functions. So it makes sense that you will see a wide variety of applications when it comes to exponential function word problems.

Exponential functions are a specific type of equation that can be used to model certain relationships that exist in the real world. In particular, exponential functions can be used to model exponential relationships, or relationships that involve rapid growth or decay by some factor. This is much different than linear functions, for example, which have a constant rate of change.

Just like any other type of function, exponential functions are awesome because they allow us to make predictions about future amounts. And who doesn’t want to predict the future!?

An exponential function word problem will ask you to do exactly this! Your goal will be to use the information provided to make a prediction about how much of something there will be in the future.

For example, you could be tasked with finding anything ranging from the amount of a substance remaining, to the value of an investment, or the size of a population of bacteria after a certain amount of time.

There are also a wide variety of exponential function word problems types. But in general, you will be given some initial amount, a growth rate or a decay rate, and an amount of time that has passed. In some cases you will also be given an exponential expression that you can use. If not, you will have to create your own exponential growth function or decay function!

## How Do You Solve Exponential Function Word Problems?

The best way to solve exponential function word problems is by using a similar problem-solving process to what you would use in any other area of mathematics.

As a first step, I always recommend reading the question carefully. This sound obvious, but reading and re-reading the problem will help you to identify any key information that is given. This will help you determine exactly what values you will be using in your solution.

For example, you should ask yourself questions such as:

- Is the problem providing a growth rate or a decay rate?
- Do I know the initial value? Or is this what I am being tasked with determining?
- Is an exponential growth function or an exponential decay function being given? Do I have to write my own function?
- What does the problem not tell me?

Once you have identified all of the key information that you are given, it is time to identify the unknown quantity that you are being asked to determine. As a tip, this is usually mentioned in the final sentence of the problem. It is important to take note of the units provided so that you can include those in your final answer as well.

Finally, your last step should be to reflect to select the appropriate problem-solving strategy. In some problems, exponential equations are provided that you can use. In other cases, you have to write your own.

Most exponential function word problems will require you to make a substitution of some sort into an exponential function. After you perform this step, you will be required to perform a few basic operations in order to determine your answer.

I have covered exponential function word problems in the past on the Math By The Pixel YouTube channel, so I have linked a video walkthrough of a series of examples. Take a look at the following video as a primer before you download and complete the exponential functions word problems worksheet with answers linked below!

## Download Your Exponential Functions Word Problems Worksheet with Answers

Below you will find an exponential functions word problems worksheet with answers. I constructed this worksheet by using the best problems that I have used throughout my teaching career to help students develop an understanding of exponential functions in the real-world.

I have hand picked a good mix of exponential growth and exponential decay problems across a wide variety of applications. For example, you will see exponential growth function examples such as compound interest and population growth. You will also see exponential decay examples such as depreciation of an asset and radioactive decay of a substance.

I also made sure to include problems that require a wide range of problem solving strategies. For example, you will be asked to use a function that is provided, as well as write and use your own!

There are also a few problems that require you to identify the meaning of each parameter in a given exponential function. This will help deepen your understanding of how these important functions work!

Remember to check the answer keys provided to ensure that you fully understand each of these problems.

**Download the worksheet by clicking below!**

## Practicing Exponential Functions Word Problems

Remember that there are a wide variety of exponential functions word problems that you can encounter. Practice is always key when it comes to mastering any mathematics concept. And exponential functions word problems are no different!

Regular practice working with exponential expression word problems will help you become more comfortable with concepts like compound interest and radioactive decay.

When you complete these types of problems often you will start to notice patterns. And before long, you will start to develop a sense of mathematical intuition about how to solve specific real-world problems!

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