This set of worksheets will give your students practice working with algebraic variables and exponents.

These worksheets show students how process exponential growth and decay. Understanding exponential growth with allow you to learn how to quantify the swelling of a population. We also look at how to calculate the rate at which that population will slowly disappear. Students work on how to solve various algebraic expressions using exponents and identify whether graphs of the results would demonstrate exponential growth or exponential decay. These worksheets demonstrate how to evaluate a variable based on the given equation, and determine if a given equation indicates exponential growth or decay based on the relationship between its variables.

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Exponential Growth and Decay Lesson

Exponential Growth and Decay Lesson

We will walk you through the basic makeup of these types of problems. Follow the steps to learn how to solve the following problem: Given r = 3t , evaluate r when t = 4.

Growth and Decay Worksheet 1

Growth and Decay Worksheet 1

There are a series of 10 problems that are all over the map with this topic. You describe how a graph of an equation may present in appearance. You will also evaluate equations.

Worksheet 2

Worksheet 2

You get more practice with this skill. We also have you learn to interpret when variables within an equations would exhibit exponential growth and decay based on their values.

Review Sheet

Review Sheet

This can also function as a homework sheet because there is a completed problem for you. You will also see problems like this: Follow the steps to determine the value of the variable based on the information given: Given a = 6b, evaluate a when b = 3.

Growth and Decay Quiz

Growth and Decay Quiz

Answer each question on this quiz and then check and score your answers. Here is an example question: Would the graph of y = 1.9x show exponential growth or exponential decay?

Class Worksheet

Class Worksheet

This is the perfect classroom worksheet to help you introduce the topic to your students. An example problem: The equation t = y2 will be an exponential growth when t equals ______.

How to Calculate Exponential Growth and Decay

There are some things in this world and universe that grow and dwindle at a ridiculously fast rate. Viruses grow at crazy rates, just look at the 2020 Corona virus scare. That simply changed medicine and the practice of it in a quarter of a year. There are other things like radioactive atoms that disintegrate so fast you can barely measure it. This indicates that things move very fast with this form of math to the point where you need to reflect on every problem that comes your way. The main goal is to understand what they are looking for. Is it an expansion from where you were at or are, they expecting you to fall back? This may require you to spend more time evaluating the parameters. It may even expect you to understand higher levels of growth or drawback to an identified part of the population.

Growth and decay models are one of the most often used uses of exponential functions. Numerous natural applications of exponential growth and decay may be found. They occur frequently in nature, from population increase and continually compounded interest to radioactive decay and Newton's law of cooling. We look into how this type can be used in the context of some of these applications in this section.

Physical quantities that rapidly vary in value or form are subject to this type of math. This concept may be used to quantify change, and the new quantity can be produced from the previous quantity.

Quantities that vary quickly experience exponential growth and decay. The idea of geometric progression has been used to infer these types of valye. Exponential growth or decay are terms used to describe quantities that vary exponentially rather than continuously.

The formula abx, where "a" stands for the beginning amount, "b" for the growth factor, which is comparable to the common ratio of the geometric progression, and "x" for the time steps for multiplying the growth factor The value of b is more than 1 (b > 1) for exponential growth and less than 1 (b 1) for exponential decline.

Studying bacterial growth, population expansion, and money growth schemes all use exponential growth. An exponential decline in a quantity over time is referred to as decay or loss. To determine realtive decay, half-life, and radioactive decay, one can utilize this type of math as well.

The rate of growth, or factor r, is used in exponential growth. The r-value in this instance is between 0 and 1 (0 r 1). You may think of the expression (1 + r) as the growth factor. And "t" stands for the time steps, or the quantity by which the growth factor must be multiplied. T can have a whole integer or a decimal value as its value. The growth factor for exponential decay is (1 - r), which has a value smaller than 1.

When calculating a number that is changing quickly, exponential functions are used in mathematics. In nature, industry, and business, there are many numbers and values that fluctuate quickly over time. Some real-world examples that need math calculations are compound internet, depreciation, viral propagation, and spoilage of perishable goods. Using the formulae f(x) = a(1 + r)t and f(x) = a(1 - r)t, these equations provides the necessary computations. Here, t is the length of time or the time factor, a is the starting quantity, r is the growth or decay constant.


Numerous routine scientific and commercial processes illustrate the idea of exponential development and decline. Let's look at a few significant uses and application of this type of math.

Internet Content

Information is exploding on the internet. Google had to gather and provide important information to the internet in the early days. But over time, internet users began to contribute content, and the amount of knowledge presently accessible on the internet is staggering. Additionally, the use of AI algorithms currently contributes to the exponential growth of the material. In a short period of time, the content is created hundreds or millions of times.

Nuclear Reactions

Nuclear fission and nuclear fission processes are two basic categories for the nuclear chain reactions. Nuclear fission may be compared to exponential decline, whereas nuclear fusion can be compared to exponential development. It is possible to watch nuclear fusion, a reaction in which two or more atoms come together to produce a bigger atom, in the sun's core. Nuclear fission is a type of exponential decay that may be seen in radioactive material. During this process, the original quantity disintegrates, and at the end of the measured time period, we have a lesser quantity.

Examples of Exponential Growth and Decay

So, is 0.5, decay or growth? In short, it is an indication of decline if the b value is between 0 and 1. It is an form of growth if the value of b exceeds 1. Because 0.5 is between 0 and 1, looking at the b value for the function shown above reveals that it decays exponentially.

Bacteria are one of the most prevalent instances of exponential development. When each bacterium divides into two new cells and so doubles in size, bacteria can grow at an alarming rate. We will have more than 16 million bacteria at the end of a day, for instance, if we start with just one microbe that can multiply by one hundredfold per hour.