Question

The table of ordered pairs (xĖy) gives an exponential function.

Write an equation for the function.
X
- 1
0
1
2

y
1
16
4
1
4

Answer 1

Answer: To write an equation for an exponential function given a table of ordered pairs, we need to find the general form of an exponential function, which is f(x) = a * b^x. Here, a and b are constants. We can find the values of a and b by using two points from the table.

Let’s use the first and second points from the table: (0, 16) and (1, 4). Substituting these values in the general form of an exponential function, we get:

16 = a * b^0 4 = a * b^1

From the first equation, we get a = 16. Substituting this value in the second equation, we get:

4 = 16 * b^1 b = 1/4

Therefore, the equation for the exponential function is f(x) = 16 * (1/4)^x.

Please note that this is just one way to find the equation for an exponential function given a table of ordered pairs. There are other methods as well.