Final answer:
The statements a, c, and d are not true regarding the two functions f(x) = 1.23x + 17 and g(x) = 0.5(1.23)^x, specifically about their rates of change.
Step-by-step explanation:
The question refers to the comparison of two functions, f(x) = 1.23x + 17 and g(x) = 0.5(1.23)^x, specifically regarding their rates of change. Let's analyze the correctness of each statement provided in the context of these functions:
- a. The rate of change of the function f(x) is never greater than the rate of change of the function g(x). This statement is not true. The function f(x) is linear with a constant rate of change of 1.23. The function g(x) is exponential, and its rate of change increases as x increases, ultimately becoming greater than that of the linear function.
- b. The rate of change of the function g(x) will eventually be greater than the rate of change of the function f(x). This statement is true. As explained above, the exponential growth of g(x) will surpass the constant rate of f(x).
- c. The rate of change of an exponential function cannot be determined. This statement is not true. The rate of change of an exponential function can be determined and is not constant—it increases or decreases depending on the base of the exponent.
- d. The rate of change of the function f(x) only appears to be the same as the rate of change of the function g(x). This statement is not true as well. The rate of change of the function f(x) is constant, whereas that of g(x) is variable and depends on the value of x.
Therefore, the statements a, c, and d are not true about the given functions.