Question

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

Explanation:

Step1: Find y-intercept (x=0)

Substitute $x=0$ into $f(x)$:
$f(0)=4(1.5)^0=4\times1=4$
So the graph passes through $(0, 4)$.

Step2: Identify growth factor

The function is in the form $f(x)=a(b)^x$, where $b$ is the growth factor. Here $b=1.5$, so each 1-unit increase in $x$ makes $y$ increase by a factor of 1.5.

Answer:

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.