The table of ordered pairs (x, y) gives an exponential function. Write an equation of the function.

Question

X Y
-1 256
0 64
1 16
2 4

Answer 1

The exponential function can be written in the form of y = a * b^x, where a is a constant and b is the base of the exponential function.

Using the given table of ordered pairs:
-1 256 = a * b^(-1)
0 64 = a * b^0
1 16 = a * b^1
2 4 = a * b^2

Since b is the base of the exponential function, we can rewrite the above equations as:
256 = a * b^(-1)
64 = a * b^0
16 = a * b^1
4 = a * b^2

Eliminating 'a' from the above equations, we get:
b = sqrt(64) = 8

Finally, we can rewrite the exponential function as:
y = 64 * 8^x