Learners will develop a foundational knowledge of functions and use them to model relationships between quantities.

MAT-12.AR.F.15 Use properties of logarithms to express the solution to abᶜᵗ = d where a, c, and dare real numbers and b is a positive real number.Evaluate the logarithm using technology when appropriate.

MAT-05.NO.NBT.07 Explain patterns in the number of zeros of the product when multiplying a number by powers of 10. Explain patterns in the placement of the decimal point when a decimal is multiplied or divided by a power of 10. Use whole-number exponents to denote powers of 10.

MAT-06.AR.EE.01 Write, read, and evaluate numerical expressions, including expressions with whole number exponents and grouping symbols.

MAT-08.AR.EE.01 Explain the relationship between repeated multiplication and the properties of integer exponents. Apply a single exponent property to generate equivalent numeric and algebraic expressions that include numerical coefficients.

MAT-09.NO.01 Explain how the definition of rational exponents follows from extending the properties of integer exponents; rewrite simple expressions involving radicals and rational exponents using the properties of exponents.

MAT-09.NO.02 Perform basic operations on simple radical expressions to write a simplified equivalent expression.

MAT-09.AR.06 Create equations and inequalities in one variable and use them to solve problems. Include equations arising from linear, quadratic, and exponential functions.

MAT-09.AR.04 Create linear and exponential equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with proper labels and scales.

MAT-09.AR.F.06 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.

MAT-0.AR.F.08 Identify situations that can be modeled with linear, quadratic, and exponential functions. Justify the most appropriate model for a situation based on the rate of change over equal intervals. Include situations in which a quantity grows or decays.

MAT-12.NO.01 Rewrite complex expressions involving radicals and rational exponents using the properties of exponents.

MAT-12.NO.02 Perform basic operations on advanced radicals and simplify radicals to write equivalent expressions.

MAT-12.AR.07 Create equations and inequalities and use them to solve problems. Include equations arising from linear and quadratic functions and simple rational and exponential functions.

MAT-12.AR.08 Create equations in two or more variables to represent relationships between quantities. Graph equations on coordinate axes with appropriate labels and scales.

MAT-12.AR.F.03 Write a function defined by an expression in different but equivalent forms to reveal and explain the different properties of the function.

MAT-12.AR.F.06 Apply the inverse relationship between exponents and logarithms to solve problems.

MAT-12.AR.F.15Use properties of logarithms to express the solution to abct = d where a, c, and d are real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.

Logarithms

MAT-12.AR.F.06 Apply the inverse relationship between exponents and logarithms to solve problems.

MAT-12.AR.F.10 Graph functions expressed symbolically and show key features of the graph by hand in
simple cases and using technology for more complicated cases.

MAT-12.AR.F.15Use the properties of logarithms to express the solution to abᶜᵗ = d where a, c, and d are
real numbers and b is a positive real number. Evaluate the logarithm using technology when appropriate.