A. The given data model represents an exponential function.
B. A function to represent the data is
.
C. The average rate of change between station 2 and station 4 is 12.
Part A.
In Mathematics, a linear function has constant rate of change (slope). Based on the data set, the slope can be calculated as follows;

Slope (m) = (8 - 4)/(2 - 1) = (16 - 8)/(3 - 2)
Slope (m) = 4 ≠ 8
An exponential function has a common ratio and this can be calculated as follows;
Common ratio =

Common ratio = 8/4 = 16/8 = 32/16
Common ratio = 2.
Part B.
Since the first term is 4 and the common ratio is 2, an exponential function that models the data set can be written as follows;

Part C.
Next, we would determine the average rate of change of the function f(x) over the interval [2, 4] by using this formula:
Average rate of change =

a = 2; f(a) = 8
b = 4; f(b) = 32
By substituting the given parameters into the average rate of change formula, we have the following;
Average rate of change = (32 - 8)/(4 - 2)
Average rate of change = 24/2
Average rate of change = 12.
Complete Question:
(1,4), (2, 8), (3, 16), (4, 32)
Part A: Do these data model represent a linear function or an exponential function? Explain your answer.
Part B: Write a function to represent the data. Show your work.
Part C: Determine the average rate of change between station 2 and station 4. Show your work.