The table represents some points on the graph of an exponential function. X:1,2,3,4 f(x):48,36,27,20.25
Answer choices: f\left(x\right)=16\left(\frac{4}{3}\right)^{x} f\left(x\right)=16\left(\frac{3}{4}\right)^{x} f\left(x\right)=64\left(\frac{4}{3}\right)^{x} f\left(x\right)=64\left(\frac{3}{4}\right)^{x}
To determine the correct exponential function that represents the points on the graph, we can first observe that the initial value of the exponential function can be found by looking at the first point where x=1. In this case, f(1) = 48.
Next, we can calculate the ratio between consecutive values of f(x) to determine the base of the exponential function. This can be done by dividing f(x) at a specific point by f(x) at the previous point.
f(2)/f(1) = 36/48 = 3/4
f(3)/f(2) = 27/36 = 3/4
f(4)/f(3) = 20.25/27 = 3/4
Since the ratio between consecutive values of f(x) is consistent and equal to 3/4, we can use this to determine the base of the exponential function. The correct function is therefore f(x) = 64*(3/4)^x.
So, the correct answer is f(x) = 64*(3/4)^x.