Question

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 three-halves, nine-eigths, StartFraction 27 Over 32 EndFraction, StartFraction 81 Over 128 EndFraction. What is the multiplicative rate of change of the function? Two-thirds Three-fourths Four-thirds Three-halves

Answer 1

Option B.

Explanation:

The given table is

x y

1
`(3)/(2)`

2
`(9)/(8)`

3
`(27)/(32)`

4
`(81)/(128)`

We need to find the multiplicative rate of change of the function.

Let multiplicative rate of change is k, then

`k=(a_2)/(a_1)`

`k=((9)/(8))/((3)/(2))`

`k=(9)/(8)* (2)/(3)`

`k=(3)/(4)`

Therefore, the correct option is B.

Answer 2

3/4

Explanation:

x | y

1 | 3/2

2 | 9/8

3 | 27/32

4 | 81/128

`((9)/(8))/((3)/(2))=(9)/(8) / (3)/(2)=(9)/(8) \cdot (2)/(3)=(18)/(24)=(18 / 3)/(24 / 3)=(6)/(8)=(6 / 2)/(8 / 2)=(3)/(4)`

So the multiplicative rate of change of this function is
`(3)/(4)` .