Maryland Math F.LE.B.6.c

MathGrades 9–12LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

The Standard

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

Apply understanding of logarithmic and logistic functions to solve real-world problems.

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 logarithms to find when an exponential model reaches a target, such as when savings hit a goal. They use logistic models to predict growth that slows near a limit.
What Mastery Looks Like: They solve 200(1.05)^t = 400 with logarithms and report about 14.2 years. Given P(t) = 1000/(1 + 9e^(-0.4t)), they find when P reaches 500 and explain why it stays below 1000.
Common Misconceptions: Students may divide 400 by 200 and stop, forgetting to solve for the exponent. They may think a logistic curve reaches its upper limit or keeps growing at the same rate forever.
How to Assess It: Exit ticket: For A(t) = 100(1.2)^t, find when A reaches 300 using logs. For P(t) = 1000/(1 + 9e^(-0.5t)), use a graph to estimate when P reaches 500 and name its upper limit.

Lesson moves

Start with five counters on a 100-square grid; each round add the count times the empty-space fraction, round additions, and graph totals.
Graph P(t) = 1000/(1 + 9e^(-0.4t)); ask, 'Can this population reach 1200? Explain using the graph and equation.'
Give pairs two cards, 200(1.05)^t = 400 and 100(1.2)^t = 300; race to solve with logs and check by substitution.
Graph M(t) = 5000/(1 + 19e^(-0.4t)) for town library signups; estimate when signups reach 4000 and explain the 5000 limit.

Free download

$Preview of the F.LE.B.6.c printable worksheet$

A ready-to-print activity worksheet aligned to F.LE.B.6.c, with an answer key for the teacher on its own page. No account needed.

PDF, US Letter, prints cleanly in black and white.

Keep exploring

Grade, subject, topic, and the complete standard are prefilled. Create one free, no account needed.