Question

What is the multiplicative rate of change of the exponential function represented in the table

Answer 1

Answer: 1.5

Explanation:

In the given picture we have a table :-

x y

1 4.5

2 6.75

3 10.125

4 15.1875

We know that exponential function is a geometric progression,

Thus for exponential function the multiplicative rate of change

`=\frac{\text{value of y at x=2}}{\text{value of y at x=1}}=(6.75)/(4.5)=1.5`

Similarly we can check

`=\frac{\text{value of y at x=3}}{\text{value of y at x=2}}=1.5`

`=\frac{\text{value of y at x=4}}{\text{value of y at x=3}}=1.5`

Therefore, the multiplicative rate of exponential function =1.5

Answer 2

We are given the following data
x y
1 4.5
2 6.75
3 10.125
4 15.1875

To get the multiplicative rate of change, we pick out two pairs of data so,
MROC = 6.75/4.5 / (2 - 1)
MROC = 1.5

The answer is 1.5