Question

which best describes the graph of the function (f(x) = 4(1.5)^x)?

• the graph passes through the point ((0, 4)), and for each increase of 1 in the (x)-values, the (y)-values increase by 1.5.
• the graph passes through the point ((0, 4)), and for each increase of 1 in the (x)-values, the (y)-values increase by a factor of 1.5.
• the graph passes through the point ((0, 1.5)), and for each increase of 1 in the (x)-values, the (y)-values increase by 4.
• the graph passes through the point ((0, 1.5)), and for each increase of 1 in the (x)-values, the (y)-values increase by a factor of 4.

Explanation:

Evaluate the y-intercept

$$
LATEXBLOCK0
$$

Determine the growth factor

$$
LATEXBLOCK1
$$

Match with the correct description

$$ \text{The graph passes through } (0, 4) \text{ and increases by a factor of } 1.5 \text{ for each unit increase in } x. $$

Answer:

• The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by 1.5.
• The graph passes through the point (0, 4), and for each increase of 1 in the x-values, the y-values increase by a factor of 1.5. (Correct answer)
• The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by 4.
• The graph passes through the point (0, 1.5), and for each increase of 1 in the x-values, the y-values increase by a factor of 4.