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.
