Consider the table that includes the input and output values of a function. -16 -13.5
-12 -10.5
-8 -7.5
-4 -4.5
0 -1.5

Which answer classifies the function using finite differences?

The function is linear with a constant first difference of –3.
The function is linear with a constant first difference of 3.
The function is quadratic with a constant second difference of –3.
The function is quadratic with a constant second difference of 3.

The correct option is;

The function is linear with a constant first difference of 3

Step-by-step explanation:

The given data on the table are;

-16            -13.5

-12            -10.5

-8              -7.5

-4              -4.5

0                -1.5

The slope of the function, m for points 1, and 3 gives;

m = (-7.5 - (-13.5))/(-8 - (-16)) = 3/4

The slope of the function, m for points 1, and 5 gives;

m = (-1.5 - (-13.5))/(0 - (-16)) = 3/4

Therefore, given that the the common difference is constant between successive points, and the slope is constant, we have that the function is linear

The first difference, which is the difference between two consecutive y-values, which are taken as the right column is given as follows;

-10.5 - (-13.5) = 3

-7.5 - (-13.5) = 3

-4.5 - (-7.5) = 3

-1.5 - (-4.5) = 3

From which we have that, the first difference constant and equal to 3

Therefore, the correct option is that the function is linear with a constant first difference of 3.

$450.00 for 6 weeks

or

$300

step-by-step explanation:

$200.00 for first week $50.00 x5 equals $250 plus $200 equals $450.00 for six weeks.

$200 for first week

$200 x 0.10 = $20

$20 x 5 = $100

$200 + $100 = $300

answer: 193

explanation:

200-7 = 193