Factor Pairing

About This Worksheet

This worksheet helps twelfth-grade Pre-Calculus students practice matching growth and decay percentages with the correct exponential factors. Students work through twelve rates and connect each one to a matching multiplier from the answer bank.

The focus is on understanding how a percent change becomes the factor used in an exponential function. A growth rate means the factor is greater than one, while a decay rate means the factor is less than one.

What Students Practice

Students practice turning percent growth into a multiplier by adding the rate to one. They also practice turning percent decay into a multiplier by subtracting the rate from one.

For example, a 6 percent growth rate matches a factor of 1.06. A 15 percent decay rate matches a factor of 0.85. The matching format helps students see these relationships quickly.

Why This Skill Matters

Students need to move comfortably between words like “grows by 12 percent” and the factor used in an equation. That conversion is one of the most important steps in building an exponential model.

This skill also helps students check their own work. If a problem says growth but the factor is less than one, something is wrong. If it says decay but the factor is greater than one, the model should be reviewed.

Common Challenges

Students may use the percent itself as the factor. Remind them that 25 percent growth does not mean a factor of 0.25. It means the original amount is kept and then increased by 25 percent, giving a factor of 1.25.

Another common mistake is using the same rule for growth and decay. Growth adds the percent to one, while decay subtracts it from one.

How To Use It

Teachers can use this worksheet as a quick matching activity before students write exponential equations from word problems. It works well for independent practice, partner work, or homework.

Parents and homeschool teachers can use one simple reminder: “Start with one whole amount.” Add the percent for growth and subtract the percent for decay.

Grade Alignment

This worksheet is intended for Grade 12 Pre-Calculus students working with exponential growth and decay. It reinforces the connection between percent rates and exponential factors.

Students should already be comfortable converting percentages to decimals. After this practice, they can evaluate exponential functions at specific inputs.