Maryland Math F.LE.B.6.b

MathGrades 9–12LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

The Standard

F.LE.B.6: Build and interpret logistic functions to model real-world problems.

Compare and contrast the exponential, logarithmic, and logistic models.

Maryland College and Career Ready Standards for Mathematics (2025) · Interpret expressions for functions in terms of the situation they model.

Teacher's field guide

What Students Need to Do: Students use graphs, tables, and situations to tell three growth patterns apart. They look at how the rate changes as the input increases and whether the output approaches a limit.
What Mastery Looks Like: A student can spot exponential growth by its constant multiplier and logistic growth by its S-shape and upper limit. They can explain why a logarithmic curve slows down but keeps rising without a fixed ceiling.
Common Misconceptions: Students may call any curve that rises quickly exponential. They may also mistake a logarithmic curve for a logistic one because both can slow down.
How to Assess It: Exit ticket: A population grows slowly, speeds up, then levels near 500. Choose a model and name one feature that rules out each of the other two.

Lesson moves

Plot three data strips on graph paper: 2,4,8,16,32; 0,7,11,14,16; 2,5,10,15,18 with a cap of 20. Compare changes between points.
Write two sentences comparing a logarithmic graph that keeps rising with a logistic graph capped at 20.
Play model match: partners sort three sketched curves and clue cards reading 'doubles,' 'slows but rises,' and 'levels near 20.'
Compare savings at 5% yearly interest, decibels as sound intensity rises, and bacteria in a petri dish with limited food. Name each model.

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