Question

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.

Answer 1

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.