Question

What is the multiplicative rate of change of the function

A) 1/3
B) 2/3
C) 2
D) 9

X. Y
1. 6
2. 4
3. 8/3
4. 16/9

Answer 1

B.
`(2)/(3)`

Explanation:

We have been given a table of values. We are asked to find the multiplicative rate of change of our given function.

Table:

x y

1 6

2 4

3 8/3

4 16/9

We know that the multiplicative rate of change of a function is the number by which each next term of an exponential function is increasing or decreasing.

We can find multiplicative rate of change by dividing any term of the function by its previous term.

`\text{Multiplicative rate of change}=(4)/(6)=(2)/(3)`

`\text{Multiplicative rate of change}=(16)/(9)/(8)/(3)=(16)/(9)*(3)/(8)=(2)/(3)`

Therefore, the multiplicative rate of change of our given function is
`(2)/(3)` and option B is the correct choice.

Answer 2

Answer: B
`(2)/(3)`

Explanation:

From the given table

When x changes from 1 to 2 , value of y changes from 6 to 4

The multiplicative rate of change=
`(4)/(6)=(2)/(3)`

Similarly we can check

When x changes from 2 to 3 , value of y changes from 4 to
`(8)/(3)`

The multiplicative rate of change=
`((8)/(3))/(4)=(2)/(3)`

When x changes from 3 to 4 , value of y changes from
`(8)/(3)` to
`(16)/(9)`

The multiplicative rate of change=
`((16)/(9))/((8)/(3))=(2)/(3)`

Therefore, the multiplicative rate of exponential function =
`(2)/(3)`