Look at this table:
x y
4
–
28.1
5
–
35.1
6
–
42.1
7
–
49.1
8
–
56.1
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine whether the given data can be modeled by a linear function or exponential function, we can calculate the ratio between consecutive y-values.
Looking at the y-values, we can see that they are increasing by 7 for each consecutive x-value. Therefore, the ratio between consecutive y-values is constant. Since the ratio is constant, we can conclude that the data can be modeled using a linear function.
To find the linear function, we need to determine the slope (m) and y-intercept (b).
The slope can be found by calculating the difference in y-values divided by the difference in x-values:
Slope (m) = (y2 - y1) / (x2 - x1) = (35.1 - 28.1) / (5 - 4) = 7 / 1 = 7
Since the data starts at x = 4 and has a corresponding y-value of 28.1, the y-intercept (b) can be determined by substituting the values into the equation y = mx + b:
28.1 = 7(4) + b
28.1 = 28 + b
b = 28.1 - 28
b = 0.1
Therefore, the linear function that models the data is:
y = 7x + 0.1