Question

Which of the following statements is true about the functions f(t) = 12(1.06)^t and g(x) = 0.52 + 3?

A) The rate of change of the function f(t) is always greater than the rate of change of the function g(x).
B) The rate of change of the function f(t) will eventually be greater than the rate of change of the function g(x).
C) The rate of change of an exponential function cannot be determined.
D) The rate of change of the function f(t) is never greater than the rate of change of the function g(x).

Answer 1

The rate of change of the function f(t) will eventually be greater than the rate of change of the function g(x)

Step-by-step explanation:

The statement that is true about the functions f(t) = 12(1.06)^t and g(x) = 0.52 + 3 is that the rate of change of the function f(t) will eventually be greater than the rate of change of the function g(x) (Option B).

To determine the rate of change of a function, we can look at the slope of the function. In function f(t), the constant multiplier 12 represents the initial rate of change, while the exponent in the function (1.06)^t represents the growth rate over time. As t increases, the exponent becomes larger, resulting in a steeper rate of change for f(t). On the other hand, function g(x) is a constant function with a slope of 0, so its rate of change remains constant.

Therefore, as time (t) increases, the rate of change of f(t) becomes greater than the rate of change of g(x).