A.SSE.3c: Transforming Exponential Functions Using Properties of Exponents: A Case Study on Interest Rates
Grade: Algebra
Domain: SSE: Seeing Structure in Expressions
Standard Description
Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15t can be rewritten as (1.151/12)12t ≈ 1.01212t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.
Domain Description
Parts of an expression, such as terms, factors, and coefficients can be interpreted individually. Complex expressions can be understood by viewing parts of it as a single unit. Through the structure of an expression, you can identify and implement rewrites. Recognition of patterns, like a difference of squares, can aid in this. Quadratic expressions can be factored to reveal the zeros of the function, or completed to reveal its maximum or minimum values. Exponential functions can be transformed using exponent properties. Similarly, the formula for a finite geometric series sum can be derived and applied to solve problems like mortgage payments.