What is the multiplicative rate of change of the function shown on the graph? Express your answer in decimal form. Round to the
2 answers:
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
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}](https://tex.z-dn.net/?f=y%3Da%28r%29%5E%7Bx%7D)
where a = initial value
x = duration or time
r = rate of change
For point (0, 2)
![2=a(r)^{0}](https://tex.z-dn.net/?f=2%3Da%28r%29%5E%7B0%7D)
a = 2
Now the exponential equation becomes ![y=2(r)^{x}](https://tex.z-dn.net/?f=y%3D2%28r%29%5E%7Bx%7D)
For the point (1, 5)
![5=2(r)^{1}](https://tex.z-dn.net/?f=5%3D2%28r%29%5E%7B1%7D)
![r=\frac{5}{2}](https://tex.z-dn.net/?f=r%3D%5Cfrac%7B5%7D%7B2%7D)
r = 2.5
Therefore, multiplicative rate of change is 2.5
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Adding both equations cancels y:
<span>4x + 8y = 16
</span><span>4x - 8y = 0
-----------------+
8x = 16 => x=2
filling in x=2 in the first equation gives:
4*2 + 8y = 16 => 8y = 8 => y=1
So (2,1) is the (x,y) pair that solves the two equations. Answer C.</span>