Question

The table represents some points on the graph of an exponential function

x 1,2,3,4 y 48,36,27,20.25

Answer 1

[AI-generated answer — Bot GPT 3.5]

To find the exponential function that models these points, we first need to determine the common ratio between consecutive y values.

Starting with y1 = 48:
y2/y1 = 36/48 = 0.75
y3/y2 = 27/36 = 0.75
y4/y3 = 20.25/27 = 0.75

Since the common ratio between consecutive y values is 0.75, we can model the function using the formula y = a * (0.75)^x.

Next, we can substitute one of the points into the formula to solve for 'a'. Let's use the point (1, 48):
48 = a * (0.75)^1
48 = 0.75a
a = 48 / 0.75
a = 64

Therefore, the exponential function that models these points is y = 64 * (0.75)^x.