Maryland Math F.LE.A.1.d

MathGrades 9–12LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

The Standard

F.LE.A.1: Distinguish between situations that can be modeled with linear functions and with exponential functions.

Distinguish between situations that can be modeled with exponential functions and logistic functions.

Maryland College and Career Ready Standards for Mathematics (2025) · Construct and compare linear, quadratic, and exponential models and solve

Teacher's field guide

What Students Need to Do: Students decide whether a situation fits constant percent change or growth that slows near a limit. They use a description, table, or graph to explain their choice.
What Mastery Looks Like: They spot a roughly constant percent change in an exponential table. They recognize a logistic graph that levels off near a realistic upper limit and explain what causes the slowdown.
Common Misconceptions: Students may call any fast-rising curve exponential, even when it levels off. They may mistake an abrupt stop at a capacity for gradual logistic growth.
How to Assess It: Exit ticket: One colony doubles hourly in fresh broth. Another grows quickly, then slows near 500 cells. Choose exponential or logistic for each and explain why.

Lesson moves

On graph paper, plot 10 calculator iterations from 5 using P × 1.5, then P + 0.5P(1 − P/100).
Write two sentences explaining why a graph that doubles early but levels off near 100 cannot stay exponential.
Sort two data cards: 3, 6, 12, 24, 48 and 3, 10, 28, 55, 78, 91; explain each choice.
Sketch how a new school app spreads among 400 students; explain why adoption may slow once most students have it.

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