Final answer:
To determine which value of x will prove that f(x) = 2^x will increase and exceed g(x) = x^2 + 5x + 6, compare the values of f(x) and g(x) for different values of x. Option D, x = 7, satisfies the given conditions.
Step-by-step explanation:
To determine which value of x will prove that f(x) = 2^x will increase and exceed g(x) = x^2 + 5x + 6, we can compare the values of f(x) and g(x) for different values of x. Starting with the given options, we can find the values of f(x) and g(x) for each choice and see which one satisfies the given conditions.
For option A, when x = 2, f(x) = 2^2 = 4 and g(x) = 2^2 + 5*2 + 6 = 4 + 10 + 6 = 20. Since f(x) < g(x), option A does not satisfy the conditions.
We can repeat this process for each option and find that option D, x = 7, satisfies the given conditions. When x = 7, f(x) = 2^7 = 128 and g(x) = 7^2 + 5*7 + 6 = 49 + 35 + 6 = 90.