Question

The exponential function f intersects the x-axis at the point (2,0) and intersects the y-axis at the point (0,-5.25) If g(x) = 3x - 2, which statement is true over the interval [0, 2]? The average rate of change of g is equal to the average rate of change of f. The average rate of change of g is greater than the average rate of change of f. The average rate of change of g is less than the average rate of change of f. The average rate of change of f cannot be determined using the information given. NextReset

Answer 1

The rate of change of g is given by its gradient, which is 3.

The average rate of change of f in [0, 2] can be calculated by taking:

$\frac{0 - (-5.25)}{2 - 0} = \frac{5.25}{2} = 2.625$

So, the average rate of change of f is less than the average rate of change of g in the interval [0, 2].

Statement 2 is correct.