Question

Look at this table:
x y
1 –2
2 –4
3 –8
4 –16
5 –32

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

Answer 1

Looking at the table, we can see that as the value of x increases, the corresponding value of y decreases exponentially. Therefore, an exponential function would be appropriate to model this data.

To find the exponential function that models the data, we need to find the values of a and b.

The formula for an exponential function is y = a(b)^x.

Let's look at the first data point: (1, -2).
Substituting the values into the equation, we get -2 = a(b)^1.

Next, let's look at the second data point: (2, -4).
Again, substituting the values into the equation, we get -4 = a(b)^2.

Now, we can solve these two equations to find the values of a and b.

From the first equation, -2 = ab.
From the second equation, -4 = ab^2.

Dividing the second equation by the first equation, we get:
-4/-2 = ab^2 / ab
2 = b

Substituting the value of b into one of the equations, we get:
-2 = a(2)^1
-2 = 2a
a = -1

Now we have found the values of a and b. Therefore, the exponential function that models the data is:
y = -1(2)^x