which best describes the graph of the function f(x) = 4(1.5)^x?\nthe graph passes through the point (0, 4)…

which best describes the graph of the function f(x) = 4(1.5)^x?\nthe graph passes through the point (0, 4), and for each increase of 1 in the x - values, the y - values increase by 1.5.\nthe 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.\nthe graph passes through the point (0, 1.5), and for each increase of 1 in the x - values, the y - values increase by 4.\nthe 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.

which best describes the graph of the function f(x) = 4(1.5)^x?\nthe graph passes through the point (0, 4), and for each increase of 1 in the x - values, the y - values increase by 1.5.\nthe 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.\nthe graph passes through the point (0, 1.5), and for each increase of 1 in the x - values, the y - values increase by 4.\nthe 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.

Answer

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.

Explanation:

Step1: Find the y - intercept

Substitute (x = 0) into (y=4(1.5)^{x}). We get (y = 4(1.5)^{0}). Since any non - zero number to the power of 0 is 1 ((a^{0}=1,a\neq0)), then (y = 4\times1=4), so the graph passes through ((0,4)).

Step2: Analyze the growth factor

The general form of an exponential function is (y = ab^{x}), where (b) is the growth factor. In the function (y = 4(1.5)^{x}), when (x) increases by 1 (from (x) to (x + 1)), we have (y_1=4(1.5)^{x}) and (y_2=4(1.5)^{x + 1}=4(1.5)^{x}\times1.5). So (\frac{y_2}{y_1}=1.5), which means the y - values increase by a factor of 1.5 for each increase of 1 in the x - values.