To determine whether the function that models the data is linear or exponential, let's first plot the given points on a coordinate plane.
The given points are: (1,3), (2,0), (3,-), (3,4), (6,5), and (9,6).
Upon plotting these points, we can see that the data does not form a straight line if we connect the points. Thus, it is unlikely that a linear function can accurately model this data.
Now, let's consider an exponential function. The general form of an exponential function is y = a * (b)^x. So, we need to find values for a and b that will fit the given points.
Upon observing the given points, we can see that the y-values decrease as the x-values increase. This indicates that the base of the exponential function should be a fraction less than 1.
Let's try a = 3 and b = 1/3.
The exponential function that models the data is y = 3 * (1/3)^x.
Now, let's determine the missing y-values:
For x = 1: y = 3 * (1/3)^1 = 3 * (1/3) = 1.
For x = 2: y = 3 * (1/3)^2 = 3 * (1/9) ≈ 0.333.
For x = 3: y = 3 * (1/3)^3 = 3 * (1/27) ≈ 0.111.
For x = 4: y = 3 * (1/3)^4 ≈ 0.037.
For x = 5: y = 3 * (1/3)^5 ≈ 0.012.
Thus, the exponential function that models the data is y = 3 * (1/3)^x.
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Write a linear function (y=mx+b) or an exponential function (y=a(b)x) that models the data.
y=
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