Question

determine if the data comes from a linear function or an exponential function. Then, enter
the equation for the function.
X=0,1,2,3,4 f(x)= 567, 189, 63, 21, 7

Answer 1

1.  The data is not linear.  There's not a constant difference between the f(x) values.  (AKA there's not a fixed slope between the data points)

2. The data is exponential, because there's a consistent ratio in the f(x) values:

     189/567 = 1/3

     63/189 = 1/3

     21/63 = 1/3

     7/21 = 1/3

Each new y-value (aka f(x)-value) is 1/3 the previous value.

Also, f(0)=567.

If we put that together, we have f(x) = 567 (1/3)^x.