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.

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

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