Growth Check Answer Key
About This Worksheet
This worksheet helps twelfth-grade Pre-Calculus students practice telling the difference between exponential relationships and non-exponential relationships. Students work with twelve examples that include equations and tables. Their job is to decide whether each relationship shows a constant multiplicative change.
The main idea is that exponential relationships grow or shrink by the same factor over equal steps. A linear relationship adds the same amount, but an exponential relationship multiplies by the same amount. This worksheet gives students a mix of examples so they can learn to spot that difference.
What Students Practice
Students practice checking whether consecutive outputs have a constant ratio. In a table, they compare one y-value to the next to see whether the values are being multiplied by the same factor each time.
They also practice recognizing exponential equations from their form. When the variable appears in the exponent and the base stays fixed, the relationship may be exponential. Equations with the variable raised to a power, such as a quadratic or cubic, are not exponential.
Why This Skill Matters
Before students can work with exponential growth and decay, they need to know when a relationship is actually exponential. This helps them choose the correct model and avoid using exponential rules on linear or polynomial situations.
The skill also helps students connect equations, tables, and patterns. An exponential function may look different in each form, but the constant multiplicative change is the feature that ties them together.
Common Challenges
Students may confuse repeated addition with repeated multiplication. Remind them that a constant difference points to a linear relationship, while a constant ratio points to an exponential one.
Another common mistake is assuming every equation with an exponent is exponential. The variable must be in the exponent. A variable squared or cubed creates a polynomial relationship instead.
How To Use It
Teachers can use this worksheet as an introduction to exponential functions or as a quick review before growth and decay. It works well for guided discussion, independent practice, homework, or a warm-up.
Parents and homeschool teachers can ask, “Are the values changing by adding the same amount, or multiplying by the same amount?” If the same multiplier keeps showing up, the pattern is exponential.
Grade Alignment
This worksheet is designed for Grade 12 Pre-Calculus students studying exponential functions. It supports recognizing exponential patterns in equations and tables and prepares students for growth and decay models.
Students should already understand ratios and basic function notation. After this practice, they can move into checking ratios directly.