About This Worksheet
This worksheet helps twelfth-grade Pre-Calculus students practice identifying whether an exponential function shows growth or decay and finding the percent rate of change. Students work through twelve functions written in standard exponential form and examine the factor being raised to the variable power.
If the exponential factor is greater than one, the function represents growth. If the factor is between zero and one, the function represents decay. Students then translate that factor into a percent increase or percent decrease.
What Students Practice
Students practice reading the growth or decay factor directly from an exponential function. They then compare that factor with one to determine whether the quantity is increasing or decreasing.
They also practice turning the factor into a percent rate. For growth, they look at how much larger the factor is than one. For decay, they look at how much smaller it is than one.
Why This Skill Matters
Growth and decay rates are used in many real-world exponential models, including population, finance, depreciation, medicine, technology, and science. Students need to understand the meaning of the factor before they can interpret the model correctly.
This skill also prepares students for writing exponential functions from verbal descriptions. Once they understand how a percent rate becomes a multiplier, they can build models more confidently.
Common Challenges
Students may confuse the exponential factor with the percent rate. For example, a factor of 1.08 represents 8 percent growth, not 108 percent growth.
Another common mistake is reading a decay factor such as 0.70 as 70 percent decay. It actually means 70 percent remains, so the decrease is 30 percent.
How To Use It
Teachers can use this worksheet after students can recognize exponential functions. It works well for guided examples, independent classwork, homework, or a quick rate review.
Parents and homeschool teachers can ask, “Is the factor above or below one?” Then compare it with one to find how much growth or decay is happening.
Grade Alignment
This worksheet is intended for Grade 12 Pre-Calculus students working with exponential growth and decay. It reinforces interpretation of exponential factors and percent rates.
Students should already understand decimal-to-percent conversion. After this practice, they can move into identifying all parts of an exponential model.