Final answer:
The function f(x)=3(2)³ˣ is equivalent to OPTION B.f(x)=24ˣ because when cubing the term (2)³, we get 8, and multiplying this by 3 gives us 24.
Step-by-step explanation:
The question involves finding an equivalent function to f(x)=3(2)³ˣ. To do this, we need to understand the process of cubing exponentials, which entails cubing the digit term normally and multiplying the exponent by 3. We see that (2)³=8, so our function simplifies to f(x)=3∙8ˣ. Thus, the equivalent function would be f(x)=24ˣ, because 3 multiplied by 8 is equal to 24. This corresponds to option B; therefore the answer is f(x)=24ˣ.
To find an equivalent function to f(x) = 3(2)³ˣ, we need to apply the rule of cubing exponentials. The rule states that we cube the digit term and multiply the exponent of the exponential term by 3. In this case, 2³ˣ = 8ˣ. So, an equivalent function would be f(x) = 3(8ˣ), which corresponds to option C.