Question

What type of function best models the data in this table? Justify your reasoning.

x 2 5 8 11 14 17
y 16 25 34 43 52 61

Answer 1

The best type of function that models the data in the table is a linear function. The linear function that best models the data is y = 3x + 10.

Step-by-step explanation:

The data in the table can be plotted on a graph to determine the best type of function that models the data. When we plot the points (x,y) from the table, we can see that they form a straight line. This indicates that a linear function would best model the data. A linear function has the form y = mx + b, where m is the slope of the line and b is the y-intercept. To find the slope, we can use any two points on the line:

Slope, m = (y2 - y1) / (x2 - x1)

Let's choose the points (2,16) and (5,25):

Slope, m = (25 - 16) / (5 - 2) = 9 / 3 = 3

Now, we can substitute the slope and one of the points into the equation y = mx + b to find the y-intercept:

16 = 3(2) + b

b = 10

Therefore, the linear function that best models the data in this table is y = 3x + 10.