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

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.

Step-by-step explanation:

We are given the function,

After the plotting the function, from the graph below, we see that,

The function passes through the point (0,4).

So, option C and D are not correct.

Moreover, we have the table,

x                                Difference in values of f(x)

1               f(1) = 6                                               f(2)-f(1) = 9-6 = 3

2              f(2) = 9                                              f(3)-f(2) = 13.5-9 = 4.5

3              f(3) = 13.5                                          f(4)-f(3) = 20.25-13.5 = 6.75                      

4              f(4) = 20.25                                            and so on

Since, the difference between the values of the functions is increasing by 'factors of 1.5'.

Thus, option B is correct.

step-by-step explanation: