Question

Approximate an x-value in which the exponential function exceeds the polynomial function.

[ f(x) = 3(3)(2x-5) ]

[ h(x) = (x + 1,5 + 4 ]

A) (x = 1)

B) (x = 2)

C) (x = 3)

D) (x = 4)

Answer 1

To approximate when the exponential function exceeds the polynomial function, it's seen that this event occurs for the first time at x = 3. So the correct answer is option C.

Step-by-step explanation:

To approximate an x-value at which an exponential function exceeds a polynomial function, we need to first correct the given functions as they seem to have typographical errors. Assuming the exponential function is f(x) = 3e^(2x-5) and the polynomial function is h(x) = x + 1.5 + 4, we shall compare them.

We're looking for the x-value where f(x) > h(x). Let's evaluate the functions at the given options:

• At x = 1, f(1) = 3e^(-3) < h(1) = 6.5
• At x = 2, f(2) = 3e^(-1) < h(2) = 7.5
• At x = 3, f(3) = 3e (1) > h(3) = 8.5
• At x = 4, f(4) = 3e^(3) > h(4) = 9.5

The exponential function f(x) exceeds the polynomial function h(x) for the first time at x = 3 (option C), as this is the smallest x-value at which f(x) > h(x).