Model Writing Answer Key

About This Worksheet

This worksheet helps twelfth-grade Pre-Calculus students practice writing exponential functions from real-world growth and decay situations. Students work through six short scenarios involving wildlife, laptop value, social media followers, medicine, savings, and machine depreciation. Each problem gives a starting amount and a percent change over time.

Students use the starting value as the initial amount and turn the percent change into an exponential factor. A growth situation uses a factor greater than one, while a decay situation uses a factor less than one. The goal is to write the model correctly, not to solve it yet.

What Students Practice

Students practice identifying the starting amount and deciding whether the situation shows growth or decay. They then convert the percent into the correct multiplier and write an exponential function.

The worksheet also reinforces the meaning of the time variable. Depending on the situation, the input may represent years, months, or hours, so students need to match the model to the context.

Why This Skill Matters

Writing an exponential model is one of the most useful skills in Pre-Calculus. Students often see real situations where a quantity grows or shrinks by the same percent over equal time periods.

This skill is useful in finance, population studies, technology, medicine, and depreciation. It helps students see how exponential functions can describe real changes over time.

Common Challenges

Students may use the percent itself as the factor. Remind them that a 6 percent increase means keeping the whole amount and adding 6 percent, so the multiplier is greater than one.

Another common mistake is using a growth factor for a decay problem. If the quantity is decreasing, the factor must be less than one.

How To Use It

Teachers can use this worksheet after students understand growth and decay factors. It works well for guided practice, independent work, homework, or a modeling lesson.

Parents and homeschool teachers can ask, “What is the starting amount?” and then, “Is the quantity growing or shrinking, and by what percent?” Those two answers lead directly to the model.

Grade Alignment

This worksheet is designed for Grade 12 Pre-Calculus students studying exponential functions and real-world modeling. It reinforces the connection between percent change and exponential equations.

Students should already understand growth and decay factors. After this practice, they can move into checking exponential models for errors.