Question

Which of the following statements is true about the functions f(x) = 0.4x + 2 and g(x) = 10(1.05)*?The rate of change of the function f(x) is always greater than the rate of change of the function g(x).. The rate of change of the function g(x) will eventually be greater than the rate of change of the function f(x).The rate of change of the function f(x) is never greater than the rate of change of the function g(x).The rate of change of an exponential function cannot be determined.

Answer 1

The rate of change of an exponential growth function increase as the x-variable increase. This means that when x tends to negative infinity, the rate of change tends to zero.

On the other hand, the rate of change of a line is constant and equal to its slope.

Therefore, the rate of change of the function g(x) will eventually be greater than the rate of change of the function f(x).