Question

What is the multiplicative rate of change of the function shown on the graph? Express your answer in decimal form. Round to the nearest tenth.

Answer 1

Multiplicative rate of change is 2.5

Explanation:

Let the given exponential function is in the form of
`y=a(r)^(x)`

where a = initial value

x = duration or time

r = rate of change

For point (0, 2)

`2=a(r)^(0)`

a = 2

Now the exponential equation becomes
`y=2(r)^(x)`

For the point (1, 5)

`5=2(r)^(1)`

`r=(5)/(2)`

r = 2.5

Therefore, multiplicative rate of change is 2.5

Answer 2

In linear models there is a constant additve rate of change. For example, in the equation y = mx + b, m is the constanta additivie rate of change.


In exponential models there is a constant multiplicative rate of change.


The function of the graph seems of the exponential type, so we can expect a constant multiplicative exponential rate.


We can test that using several pair of points.


The multiplicative rate of change is calcualted in this way:

[f(a) / f(b) ] / (a - b)

Use the points given in the graph: (2, 12.5) , (1, 5) , (0, 2) , (-1, 0.8)

[12.5 / 5] / (2 - 1) = 2.5


[5 / 2] / (1 - 0) = 2.5


[2 / 0.8] / (0 - (-1) ) = 2.5


Then, do doubt, the answer is 2.5