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weqwewe [10]
3 years ago
10

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.

Mathematics
2 answers:
allsm [11]3 years ago
6 0
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





Goryan [66]3 years ago
4 0

Answer:

Multiplicative rate of change is 2.5

Step-by-step 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=\frac{5}{2}

r = 2.5

Therefore, multiplicative rate of change is 2.5

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