Look at this table:
x y
–
2 10
–
1 2
0
–
6
1
–
14
2
–
22
Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
To determine whether a linear function or an exponential function models the given data, let's first plot the points on a graph.
x | y
-------
-2 | 10
-1 | 2
0 | -6
1 | -14
2 | -22
Based on the plot, it appears that a linear function is not an appropriate model since the data points do not fall on a straight line. Instead, the data seems to follow an exponential pattern.
To determine the exponential function that models the data, we can try to find the general form of the equation: y = a(b)^x.
First, let's find the value of "a." We can select any point in the table to substitute into the equation. Let's use the point (0, -6). Plugging these values into the equation allows us to solve for "a":
-6 = a(b)^0
-6 = a * 1
a = -6
Next, let's find the value of "b." We can use any other point in the table. Let's use the point (1, -14):
-14 = -6(b)^1
-14 = -6b
b = -14 / -6
b = 7/3
Now that we have the values of "a" (-6) and "b" (7/3), we can write the exponential function that models the data:
y = -6 * (7/3)^x
Therefore, the exponential function that models the given data is y = -6 * (7/3)^x.