Given the table below, determine if the data represents a linear or an exponential function and find a possible formula for the function. x 0 1 2 3 4 f(x) 0 2 4 6 8 a. Exponential; y = 1 (1.2) Superscript x c. Exponential; y = 2 (1.1) Superscript x b. Linear; y = 2x d. Linear; y = x

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x 0 1 2 3 4

f(x) 12.5 13.75 15.125 16.638 18.301

If the change in x values and change in y values are constant then the data will be linear.

So, change in x from 0 to 1 is 1-0=1

Similarly change in x from 1 to 2 is 2-1=1

So, change in x's is constant in the given data.

Now let's check for change in y values.

Change in y from 12.5 to 13.75 is 13.75-12.5=1.25

Similarly change in y from 13.75 to 15.125 is 15.125-13.75=1.375

Changes in y's are not constant.

So, the given data is not linear.

Let's assume the exponential function is:

Let's take any two points from the data and plug into the above equation to get the equation. Let's plug in the first point (0, 12.5) in the above function. So,

Since

So, a=12.5

Next step is to plug in the second point (1, 13.75) and a=12.5 in the same equation to get the value of b. Hence,

13.75=12.5b

Dividing each sides by 12.5.

So, b=1.1

Now we can plug in the value of a and b to get the exponential formula. Hence,

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