Problem preview

F-IF.8.b Warmup M2-024-A05-V03

Use exponent properties to interpret exponential expressions, including percent growth and decay.

Compare two exponential expressions for equivalence by rewriting one with exponent rules

Problem

Compare exponential expressions \(10(0.5)^t\) and \(10(2)^t\) for equivalence.

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Yes, they are equivalent because 0.5 and 2 are related, so raising them to the same power t gives the same result with the same coefficient 10.

Yes, they are equivalent because 0.5t can be rewritten as 2t, so both expressions are really 10(2)t.

No, they are not equivalent because 10(0.5)t means 10· 0.5t, while 10(2)t means 10· 2t, so the expressions are different.

No, they are not equivalent because 10(0.5)t = 10(2⁻¹)t = 10(2)⁻t, which is not the same as 10(2)t.

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Curriculum context

Course: Math II
Standard: F-IF.8.b
Category: Functions
Domain: Interpreting Functions
Objective: Use exponent properties to interpret exponential expressions, including percent growth and decay.
Problem type: Compare two exponential expressions for equivalence by rewriting one with exponent rules