Maryland Math F.LE.A.4.a

MathGrades 9–12LINEAR, QUADRATIC, AND EXPONENTIAL MODELS

The Standard

F.LE.A.4: For exponential models, express as a logarithm the solution to ab^(ct) = d where a, c, and d are numbers and the base b is 2, 10, or e; evaluate the logarithm using technology.

Use properties of logarithms, including both common and natural logarithms, to rewrite and solve exponential models.

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 isolate the exponential part of a growth or decay model. They use log or ln to move the unknown out of the exponent, solve, and explain what the answer means.
What Mastery Looks Like: Given 200(1.15)^t = 500, students write t = log(2.5)/log(1.15) = ln(2.5)/ln(1.15). They find about 6.6 hours and check it in the original model.
Common Misconceptions: Students may write log(1.15^t) as log(1.15)^t instead of t log(1.15). They may mix log and ln in one fraction or forget to isolate the exponential term first.
How to Assess It: A culture starts with 200 cells and grows 15% each hour. When will it reach 500 cells? Show your log or ln step.

Lesson moves

Build piles of 1, 2, 4, 8, and 16 counters; use logs to find when the pile reaches 64.
For 120(1.08)^t = 200, solve once with log and once with ln; explain why the answers match.
Give pairs cards with equations, isolated exponential terms, and log solutions; have them match sets and check by substitution.
Use a 4% yearly savings rate to model when $1,000 reaches $1,500; solve and round to the next full year.

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