Florida B.E.S.T. MA.912.AR.5
B.E.S.T. Standard (Benchmark Cluster)
Write, solve and graph exponential and logarithmic equations and functions in one and two variables.
Florida B.E.S.T. Standards for Mathematics
Cluster contents
Benchmarks in This Standard
MA.912.AR.5 is a B.E.S.T. standard. These are the benchmarks under it.
- MA.912.AR.5.1
Solve one-variable exponential equations using the properties of exponents.
- MA.912.AR.5.2
Solve one-variable equations involving logarithms or exponential expressions. Interpret solutions as viable in terms of the context and identify any extraneous ...
- MA.912.AR.5.3
Given a mathematical or real-world context, classify an exponential function as representing growth or decay.
- MA.912.AR.5.4
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 ...
- MA.912.AR.5.5
Given an expression or equation representing an exponential function, reveal the constant percent rate of change per unit interval using the properties of expon...
- MA.912.AR.5.6
Given a table, equation or written description of an exponential function, graph that function and determine its key features.
- MA.912.AR.5.7
Solve and graph mathematical and real-world problems that are modeled with exponential functions. Interpret key features and determine constraints in terms of t...
- MA.912.AR.5.8
Given a table, equation or written description of a logarithmic function, graph that function and determine its key features.
- MA.912.AR.5.9
Solve and graph mathematical and real-world problems that are modeled with logarithmic functions. Interpret key features and determine constraints in terms of t...
Teacher's field guide
What This Cluster Means
What Students Need to Do
- Students write exponential and logarithmic models from graphs, tables, and word problems. They solve equations in one variable and graph related equations in two variables. They connect exponential functions with their logarithmic inverses.
What Mastery Looks Like
- Students create equations from tables, graphs, and situations, then solve them using equivalent forms or logarithms. They graph accurately and identify intercepts, asymptotes, domain, range, growth, and decay. They check solutions against logarithm restrictions and the original equation.
Common Misconceptions
- Students may treat a logarithm as division or incorrectly split log(a + b). They may allow zero or negative logarithm inputs, draw graphs across asymptotes, or miss extraneous solutions. Some confuse exponential growth with linear growth because both graphs increase.
How to Assess It
- Give this exit ticket: For y = 3(2^x), graph the function, state its asymptote, domain, and range, write its inverse, then solve 3(2^x) = 24.
Lesson moves
Ways to Teach It
Use graphing transparencies to overlay y = 2^x, y = log₂(x), and y = x, then mark matching inverse points.
Ask students to explain why log₂(8) = 3 and why log₂(0) has no real value.
Run a card sort matching equations, graphs, tables, domains, ranges, and asymptotes for exponential and logarithmic functions.
Model a savings account or bacteria culture, write an exponential equation, then use logarithms to find when a target value is reached.
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Printable MA.912.AR.5 Worksheet
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Related Standards
- MA.912.AR.3
Write, solve and graph quadratic equations, functions and inequalities in one and two variables.
- MA.912.AR.4
Write, solve and graph absolute value equations, functions and inequalities in one and two variables.
- MA.912.AR.6
Solve and graph polynomial equations and functions in one and two variables.
- MA.912.AR.2
Write, solve and graph linear equations, functions and inequalities in one and two variables.
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