Look at the table:

Question

X y
1 -12
2 -36
3 -108
4 -324
5 -972

Write a linear function (y = mx + b) or an exponential function (y = a(b)^x) that models the data.

y = blank

Answer 1

To determine if the function is linear or exponential, let's first examine the relationship between x and y.

When x increases by 1, y is multiplied by -3. Therefore, the relationship between x and y is exponential.

To find the exponential function that models the data, we can observe that y is equal to -12 when x is equal to 1. This gives us the base of the exponential function, which is -12.

Now, let's plug in the second data point (x=2, y=-36) into the general exponential form, y = a(b)^x, to find the value of b:

-36 = -12(b)^2

Dividing both sides of the equation by -12:

3 = (b)^2

Taking the square root of both sides:

b = √3

The exponential function that models the data is:

y = -12(√3)^x