Florida B.E.S.T. MA.912.AR.5.7
The Standard
Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine constraints in terms of the context.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students use exponential equations and graphs to answer questions about growth and decay. They identify key features, solve for values or times, and choose domain and range limits that make sense in context.
What Mastery Looks Like
- Students graph an exponential model and identify its initial value, growth or decay rate, intercept, and asymptote. They solve for an unknown value or time and restrict the domain and range to fit the situation.
Common Misconceptions
- Students may treat the growth factor as the percent rate, confusing 1.08 with 8%. They may ignore the initial value, use a linear model, or include negative time and impossible output values.
How to Assess It
- Give students P(t) = 800(1.06)^t for an investment. Ask them to graph 0 ≤ t ≤ 10, find when it exceeds $1,200, and interpret each key feature.
Lesson moves
Ways to Teach It
Have groups repeatedly shake 50 two-sided counters, remove one color, record survivors, and graph the resulting decay data.
Ask students to compare two savings plans and write which grows faster, when it overtakes the other, and how the graphs show this.
Run a card sort matching exponential equations, graphs, tables, growth rates, initial values, and reasonable context constraints.
Use a used-car value table to build a decay model, predict future value, and explain why negative time or value is unreasonable.
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