Look at the table:
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
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