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Yelena assets that expressions for the exponential functions g(x) = 7 (1.5) ^4x. and h(x) = 7(5.0625) ^ x are equivalent. Show and explain why she is, or is not, correct.

User Kelly
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1 Answer

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11 votes

Answer:

Yelena is correct.

Explanation:

Yelena asserts that the two functions:


g(x)=7(1.5)^(4x)\text{ and } h(x)=7(5.0625)^x

Are equivalent.

She is indeed correct. Recall the power of a power property for exponents:


(x^a)^b=x^(ab)

Therefore, we can rewrite function g as:


g(x)=7((1.5)^4)^x

Evaluate the inner expression:


1.5^4=5.0625

Therefore:


g(x)=7(5.0625)^x=h(x)

Hence, Yelena is correct.

User Reymond
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