Florida B.E.S.T. MA.912.AR.5.4
The Standard
Write an exponential function to represent a relationship between two quantities from a graph, a written description or a table of values within a mathematical or real-world context.
Florida B.E.S.T. Standards for Mathematics
Teacher's field guide
What This Standard Means
What Students Need to Do
- Students identify the initial value and repeated multiplication factor in a table, graph, or situation. They use these values to write a function in the form f(x) = a(b)^x and interpret each parameter.
What Mastery Looks Like
- A student finds the output when x = 0 and the common multiplier for equal input intervals. They write a correct function, define the variables, and check it against the given values or graph.
Common Misconceptions
- Students may use constant differences instead of constant ratios, treating exponential data as linear. They may swap the initial value and base, or use 20% instead of 1.20 for 20% growth.
How to Assess It
- Give the table x: 0, 1, 2, 3 and y: 5, 15, 45, 135. Ask students to write the function and label the initial value and growth factor.
Lesson moves
Ways to Teach It
Have pairs double or halve a pile of counters each round, record the totals, and write the matching exponential function.
Ask students to explain why a 15% yearly decrease uses a base of 0.85 rather than 0.15.
Give groups cards showing equations, tables, graphs, and stories, then have them match each set and justify one match.
Use a savings account with annual compound interest, then have students identify the starting balance, growth factor, and function.
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Related Standards
- MA.912.AR.5.6
Given a table, equation or written description of an exponential function, graph that function and determine its key features.
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Write, solve and graph exponential and logarithmic equations and functions in one and two variables.
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