A-SSE.2.3.c

Choose and produce an equivalent form of an expression to reveal and explain properties of the quantity represented by the expression.

Use the properties of exponents to transform expressions for exponential functions. For example the expression 1.15^t can be rewritten as (1.15^(1/12))^12t ≈1.012^12t to reveal the approximate equivalent monthly interest rate if the annual rate is 15%.

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Students are asked to use the properties of exponents to show that two expressions are equivalent and compare the two functions in terms of what each reveals.
Population Drop
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Students are asked to transform an exponential expression so that the rate of change corresponds to a different time interval.
College Costs
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Virtual/Hands-on Manipulatives
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Hook/Performance Tasks
Math Literature
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There are many different ways to write exponential expressions that describe the same quantity, in this task the amount of a radioactive substance after t years. Depending on what aspect of the context we need to investigate, one expression of the quantity may be more useful than another. This task contrasts the usefulness of four equivalent expressions. Students first have to confirm that the given expressions for the radioactive substance are equivalent. Then they have to explain the significance of each expression in the context of the situation.
Forms of Exponential Expressions
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This context makes for an interesting application of calculating interest.
How Much Did Peterson Lose By Not Cashing His Check?
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This task illustrates the process of rearranging the terms of an expression to reveal different aspects about the quantity it represents, precisely the language being used in standard MAFS.912.A-SSE.2.3. Students are provided with an expression giving the temperature of a container at a time t, and have to use simple inequalities (e.g., that 2t>0 for all t) to reduce the complexity of an expression to a form where bounds on the temperature of a container of ice cream are made apparent.
Ice Cream
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The purpose of this task is to help students see manipulation of expressions as an activity undertaken for a purpose.
Increasing or Decreasing? Variation 2