Florida B.E.S.T. MA.912.AR.5.5
The Standard
Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of exponents. Interpret the constant percent rate of change in terms of a real-world context.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use exponent rules to rewrite an exponential expression in the form a(b)^x, where b shows the multiplier for one unit. They convert b to a percent rate using (b − 1) × 100% and explain what that rate means in context.
What Mastery Looks Like
- A student can recognize that 3^(x/2) has a one-unit factor of √3 and that 8(0.9)^(2x) has a factor of 0.81. They identify about 73.2% growth in the first example and 19% decay in the second, using correct units.
Common Misconceptions
- Students often report the multiplier as the percent, so a factor of 1.06 becomes 1.06% instead of 6%. They may ignore a scaled exponent, use its visible base as the one-unit factor, or label any factor below 1 as negative growth.
How to Assess It
- Exit ticket: For P(t) = 1200 × 4^(t/2), where t is years, rewrite the expression to show the one-year multiplier, find the annual percent rate, and interpret it.
Lesson moves
Ways to Teach It
Give groups cards showing expressions, one-unit factors, and percent rates; students match sets and justify each match with an exponent rule.
Pose the claim that 5(1.21)^(t/2) grows 21% yearly; students write a claim, calculation, and context sentence.
Run a relay where teams rewrite one expression, calculate its percent rate, then check another team’s work before advancing.
Use a two-year population growth report to build P(t) = P0(k)^(t/2), then find and explain the equivalent annual rate.
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