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:

Find the y-intercept

Using the Exponential Growth Model knowledge point

$$ f(0) = 4(1.5)^0 = 4(1) = 4 \implies (0, 4) $$

Determine the growth factor

Using the Exponential Growth Model knowledge point

$$ \frac{f(x+1)}{f(x)} = \frac{4(1.5)^{x+1}}{4(1.5)^x} = 1.5 $$

Answer:

• (A) 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.
• (B) 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)
• (C) 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.
• (D) 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.