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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.

Sagot :

xKelvin

Answer:

Yelena is correct.

Step-by-step explanation:

Yelena asserts that the two functions:

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

Are equivalent.

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

[tex](x^a)^b=x^{ab}[/tex]

Therefore, we can rewrite function g as:

[tex]g(x)=7((1.5)^4)^x[/tex]

Evaluate the inner expression:

[tex]1.5^4=5.0625[/tex]

Therefore:

[tex]g(x)=7(5.0625)^x=h(x)[/tex]

Hence, Yelena is correct.

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