The
<u>correct answers</u> are:
The <u>first table is linear</u>.
The <u>second table is exponential</u>.
Explanation:
To see if a set of data is linear, we find the <u>slope</u>. Slope is given by the formula
.
We check each pair of points in the <u>first table</u>. The slope between the <u>first two points</u> is:
The slope between the <u>second two points</u> is:
The slope between the <u>third two points</u> is:
Since the slope is the <u>same </u>between any two pairs of points, this is a <u>linear </u>set of data.
Checking each pair of points in the <u>second table</u>, we have:
for the <u>first two points</u>.
For the <u>second pair of points</u>, we have:
Since the slope is <u>not the same</u> between each pair of points, we know the data is <u>not linear.</u>
Next we will check the <u>second table</u> to see if it is <u>quadratic</u>. Since the x-coordinates go up the same number each time, we can check the y-coordinates, specifically looking at the <u>second differences</u>.
For the <u>second differences</u>, we first find the difference between each y-value:
1-0=1
4-1=3
8-4=4
Now we find the <u>difference between each first difference</u>:
3-1=2
4-3=1
Since these second differences are <u>not the same</u>, the data is <u>not quadratic</u>.
From <u>graphing </u>the data in the table, we can see that the data in the second table is <u>exponential</u>.