What is the multiplicative rate of change of the function? The table represents an exponential function.

A 2-column table has 4 rows. The first column is labeled x with entries 1, 2, 3, 4. The second column is labeled y with entries 0.25, 0.125, 0.0625, 0.03125.

The multiplicative rate of change of the function is 0.5

The multiplicative rate of change of the function is 0.5

Explanation:

The multiplicative rate of change is the ratio between consecutive entries.

Naming r the multiplicative rate of change, if it is constant you get:

r = second entry / first entry = third entry / second entry = fourth entry / third entry.

Here:

second entry / first entry = 0.125 / 0.25 = 0.5 third entry / second entry = 0.0625 / 0.125 = 0.5 fourth entry / third entry = 0.03125 / 0.0625 = 0.5

Thus, the multiplicative rate of change is 0.5. It means that you can obtain each entry as the product of the previous entry times 0.5:

0.25 * 0.5 = 0.125 0.125 * 0.5 = 0.0625 0.0625 * 0.5 = 0.03125

In general, exponential functions have constant multiplicative rate of changes.