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Answer:

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Step-by-step explanation:

Answer:

Exponential

Step-by-step explanation:

Using the linear function formula for x,y

[tex] y = mx + b[/tex]

where m is the slope and y is the y intercept.

Using the exponential function for x and y

[tex]y = ab {}^{x} [/tex]

where a is the initial value, b is the factor.

We would plug the follow x and y values into the table to see if it true for all of the other x and y values.

To keep thing short, linear function is not the answer becuase the function doesnt Maintain a consistent average rate of change so it cant be that.

Let see if it a exponential function.

plug in 0 and -2 into exponetial formula

[tex] - 2 = ab {}^{0} [/tex]

[tex] - 2 = a[/tex]

Now, let use another pair of point to see if this is true.

[tex]y = - 2b {}^{x} [/tex]

Use 1 and -6

[tex] - 6= - 2b {}^{1} [/tex]

[tex]3 = b {}^{1} [/tex]

Our exponetial equation is

[tex]y = - 2(3) {}^{x} [/tex]

Let plug in -2,18 to see if it true.

[tex] - 18 = - 2(3) {}^{2} [/tex]

[tex] - 18 = - 2 \times 9[/tex]

[tex] - 18 = - 18[/tex]

so it is exponential