Question

The table represents an exponential function.

X12
3
4
ហស ~ <|
125
What is the multiplicative rate of change of the
function?
O
0 00
2

Answer 1

The multiplicative rate of change of the function is 2/5.

The multiplicative rate of change of an exponential function can be found by examining how the function's output changes for a one-unit increase in the input.

In the given table, the function represents an exponential decay, as the values of y decrease as x increases. The constant multiplicative rate of change for exponential decay can be found by taking the ratio of any output to the previous output for a one-unit increase in the input.

Using the given table:

For x=1, y=2

For x=2, y=3

For x=3, y=2/25

For x=4, y=2/125

The multiplicative rate of change can be found by taking the ratio of each output to the previous output:

For x=2, the multiplicative rate of change is 3/2

For x=3, the multiplicative rate of change is (2/25) / 3 = 2/75

For x=4, the multiplicative rate of change is (2/125) / (2/25) = 2/5

Therefore, the multiplicative rate of change of the function is 2/5.