Look at this table:
x y
–
3 0.13
–
2 2.71
–
1 5.29
0 7.87
1 10.45
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
To determine if the given data can be modeled by a linear or exponential function, we need to examine the relationship between the x-values and y-values.
Looking at the x-values, we can see that they increase by a constant increment of 1: -3, -2, -1, 0, 1.
Looking at the y-values, we can see they increase by a constant increment as well: 0.13, 2.71, 5.29, 7.87, 10.45.
Since both the x-values and y-values increase by a constant increment, the data can be modeled by a linear function.
Now, we can calculate the slope (m) and y-intercept (b) for the linear function using any two points from the table.
Let's use the points (0, 7.87) and (1, 10.45):
Slope (m) = (Change in y) / (Change in x)
= (10.45 - 7.87) / (1 - 0)
= 2.58
Now, we can use the slope and one of the points to find the y-intercept (b):
Using the point (1, 10.45):
10.45 = (2.58)(1) + b
10.45 = 2.58 + b
b = 10.45 - 2.58
b = 7.87
Therefore, the linear function that models the data is:
y = 2.58x + 7.87