Question

Which of the following statements is true for a function with equation f(x) = 5(3)*?

The graph has y-intercept (0,5) and increases with a constant ratio of 3.
The graph has y-intercept (0, 3) and decreases with a constant ratio of 3.
The graph has y-intercept (0, 3) and increases with a constant ratio of 5.
The graph has y-intercept (0,5) and decreases with a constant ratio of 3.

Answer 1

The graph has y-intercept (0,5) and increases with a constant ratio of 3

Answer 2

The graph has y-intercept (0,5) and increases with a constant ratio of 3

Explanation:

The value of the function when x=0 is 5·3^0 = 5, so the y-intercept is (0, 5).

Each increase of 1 in x causes the function value to increase by a factor of 3, so the 'constant ratio' is 3. (That is the base of the exponential term.)