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

Answer:

Yelena is correct.

Step-by-step 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.