From the table below, determine whether the data shows an exponential function. explain why or why not.

x: 3, 6, 9, 12
y: 1, 2, 4, 8

(a) no; the domain values are at regular intervals.
(b) no; a different value is added to each range value.
(c) no; there is no relationship between the x value and it's corresponding y value.
(d) yes; the domain values are at regular intervals and the range values have a common factor 2.

Option D is correct

Yes; the domain values are at regular intervals and the range values have a common factor 2

Step-by-step explanation:

Exponential function is given by:

....[1] where, a is the initial values and b  is common factor or growth factor

As per the statement:

x             y

3             1

6             2

9             4

12             8

Consider any two points i.e,

(3, 1) and (6, 2)

Substitute these in [1] we have;

               ......[2]

              .....[3]

Divide equation [3] by [2] we get;

⇒

Substitute this value in [2] we have;

⇒

Divide both sides by 2 we have;

Substitute the given values in [1] we have;

⇒

This is an exponential function.

The domain values(i.e x -coordinates) are at regular intervals and the range values (i.e y-coordinates) have a common factor 2.

in problems involving proportions, we can use cross products to test whether two ratios are equal and form a proportion. to find the cross products of a proportion, we multiply the outer terms, called the extremes, and the middle terms, called the means.

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