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3 years ago

Arrange these functions from the greatest to the least value based on the average rate of change in the specified interval.

Mathematics

1 answer:

Romashka [77]3 years ago

5 0

By definition, the average change of rate is given by:
$AVR = \frac{f(x2)-f(x1)}{x2-x1}$
We will calculate AVR for each of the functions.
We have then:

f(x) = x^2 + 3x interval: [-2, 3]:
$f(-2) = x^2 + 3x = (-2)^2 + 3(-2) = 4 - 6 = -2

f(3) = x^2 + 3x = (3)^2 + 3(3) = 9 + 9 = 18$
$AVR = \frac{-2-18}{-2-3}$
$AVR = \frac{-20}{-5}$
$AVR = 4$

f(x) = 3x - 8 interval: [4, 5]:
$f(4) = 3(4) - 8 = 12 - 8 = 4 f(5) = 3(5) - 8 = 15 - 8 = 7$
$AVR = \frac{7-4}{5-4}$
$AVR = \frac{3}{1}$
$AVR = 3$

f(x) = x^2 - 2x interval: [-3, 4]
$f(-3) = (-3)^2 - 2(-3) = 9 + 6 = 15

f(4) = (4)^2 - 2(4) = 16 - 8 = 8$
$AVR = \frac{8-15}{4+3}$
$AVR = \frac{-7}{7}$
$AVR = -1$

f(x) = x^2 - 5 interval: [-1, 1]
$f(-1) = (-1)^2 - 5 = 1 - 5 = -4

f(1) = (1)^2 - 5 = 1 - 5 = -4$
$AVR = \frac{-4+4}{1+1}$
$AVR = \frac{0}{2}$
$AVR = 0$

Answer:
these functions from the greatest to the least value based on the average rate of change are:
f(x) = x^2 + 3x
f(x) = 3x - 8
f(x) = x^2 - 5
f(x) = x^2 - 2x

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Answer:

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So the calculated value is 0.9 points above the actual value.

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And the calculated value it's 0.537% higher than the actual value.

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Step-by-step explanation:

Data given

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Notation

Let CPI the dependent variable y. And the time th independent variable x.

For this case we want to adjust a linear model givn by the following expression:

$y=mx+b$

Solution to the problem

Part a

For this case we can find the slope with the following formula:

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And if we replace we got:

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Part b

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$y = 3.8(18) +100=168.4$

And the actual value is 167.5 we can compare the result using absolute change or relative change like this:

$Abs. change= |168.4-167.5|=0.9$

So the calculated value is 0.9 points above the actual value.

And we can find also the relative change like this:

$Relative. Change =\frac{|Calculated -Real|}{Real}x100$

And if we replace we got:

$Relative. Change =\frac{|168.4 -167.5|}{167.5}x100 =0.537$ %

And the calculated value it's 0.537% higher than the actual value.

Part c

For this case we can use the slope obtained from the linear model to answer this question, and we can conclude that the CPI is increasing at approximate 3.8 units per year.

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