Question

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.

Answer 1

The multiplicative rate of change of the function is 0.5

Step-by-step explanation:

Answer 2

• The multiplicative rate of change of the function is 0.5

Step-by-step 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.