Question

Look at this table:
x y
3 21.58
4 30.15
5 38.72
6 47.29
7 55.86
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=

Answer 1

To determine whether the data can be modeled using a linear function or an exponential function, we can look at the relationship between the x-values and the corresponding y-values.

Looking at the given data, we can observe that as the x-values increase, the corresponding y-values also increase. This suggests that the data may be more appropriately modeled using a linear function.

To find the linear function that models the data, we need to find the slope (m) and the y-intercept (b).

We can calculate the slope (m) using the formula:
m = (change in y) / (change in x)

Using the first and last data points, we can calculate the change in y:
change in y = 55.86 - 21.58 = 34.28

Similarly, we can calculate the change in x:
change in x = 7 - 3 = 4

Now, we can calculate the slope (m):
m = (34.28) / (4) = 8.57

Thus, the slope (m) is 8.57.

To find the y-intercept (b), we can substitute the values of any of the points (x, y) into the linear equation y = mx + b and solve for b.

Let's use the point (3, 21.58):

21.58 = (8.57)(3) + b
21.58 = 25.71 + b
b = 21.58 - 25.71
b = -4.13

Thus, the y-intercept (b) is -4.13.

Now that we have found the slope (m) and the y-intercept (b), we can write the linear function using the equation y = mx + b:

y = 8.57x - 4.13