Question

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) 18 14 10 6 2 a. Exponential; c. Exponential; b. Linear; y = 18x - 4 d. Linear; -4x + 18 Please select the best answer from the choices provided A B C D

Answer 1

Answer:

option d.

Step-by-step explanation:

We have the following set of data:

x     0   1    2   3  4

f (x)   18 14  10 6  2

Let's assume the function is linear, then, the equation of the line would ne:

(y - y0) = m(x-x0)

where m= (y1-y0) / (x1-x0)

And (x1, y1) = (1, 14)

(x0, y0) = (0, 18)

You can choose any of the points given in the set of data.

Then,

m = (14-18)/(1-0) = -4.

Then the equation of the line is:

(y - 18) = -4x

y = -4x + 18.

If the function is linear, then all the points given in the set of data will satisfy the function. Let's try:

(2, 10):

10 = -4(2) + 18.

10 = 10

SATISFIES THE EQUATION

(3, 6):

6 = -4(3) + 18.

6 = 6

SATISFIES THE EQUATION

(4, 2)

2 = -4(4) + 18.

6 = 6

SATISFIES THE EQUATION

So, the function is linear. And the correct option is option d.