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4 years ago

The graph below shows the average Valentine’s Day spending between 2003 and 2012

Mathematics

1 answer:

Lapatulllka [165]4 years ago

7 0

The average rate of change of a graph between two intervals is given by the difference in value of the values on the graph of the two interval divided by the difference between the two intervals.

Part A.

From the graph the average Valentine's day spending in 2005 is 98 while the average Valentine's day spending in 2007 is 120.

The average rate of change in spending between 2005 and 2007 is given by

$\frac{120-98}{2007-2005} = \frac{22}{2} =\$11/year$

Part B

From the graph the average Valentine's day spending in 2004 is 100 while the average Valentine's day spending in 2010 is 103.

The average rate of change in spending between 2004 and 2010 is given by

$\frac{103-100}{2010-2004} = \frac{3}{6} =\$0.5/year$

Part C:

From the graph the average Valentine's day spending in 2009 is 102 while the average Valentine's day spending in 2010 is 103.

The average rate of change in spending between 2009 and 2010 is given by

$\frac{103-102}{2010-2009} = \$1/year$

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Drag the tiles to the correct boxes to complete the pairs. Not all tiles will be used. Find the average rate of change of each f

Naya [18.7K]

Each representation is matched with its respective average rate of change as follows:

h(x) ⇒ 4
f(x) ⇒ 5
g(x) ⇒ 2
j(x) ⇒ -6

<h3>What is a rate of change?</h3>

A rate of change is also referred to as slope and it can be defined as a type of function that describes the average rate at which a quantity decreases or increases with respect to another quantity.

<h3>How to calculate the rate of change?</h3>

Mathematically, the rate of change for a function can be calculated by using this expression;

$Slope = \frac{Change\;in\;y\;axis}{Change\;in\;x\;axis}\\\\Slope = \frac{y_2\;-\;y_1}{x_2\;-\;x_1}$

Thus, the average rate of change over the given interval [a, b] is given by:

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

Where:

The interval is [0, 2], so a = 0 and b = 2

Substituting the given parameters into the formula, we have;

r = [f(2) - f(0)]/(2 - 0)

r = [f(2) - f(0)]/2

For the first function h(x), we have:

r = [h(2) - h(0)]/2

When x = 2

h(2) = 2² + 2(2) - 6

h(2) = 4 + 4 - 6

h(2) = 2.

When x = 0

h(0) = 0² + 2(0) - 6

h(0) = 0 + 0 - 6

h(0) = -6.

Evaluating the function, we have:

r = [h(2) - h(0)]/2

r = [2 - (-6)]/2

r = (2 + 6)/2

r = 8/2

r = 4.

For the second function f(x), we have:

Note: The x-intercept is at (2, 0), so x = 2 and f(2) = 0 while its y-intercept at (0, -10), so x = 0, f(0) = -10

r = [f(2) - f(0)]/2

r = [0 - (-10)]/2

r = (0 + 10)/2

r = (10)/2

r = 5.

For the third function g(x), we have:

Note: g(2) = 6 and g(0) = 2 on the graph.

r = [g(2) - g(0)]/2

r = (6 - 2)/2

r = 4/2

r = 2.

For the fourth function j(x), we have:

Note: From the table, x = 2 outputs j(2) = -8 while x = 0 outputs j(0) = 4.

r=[j(2) - j(0)]/2

r = (-8 - 4)/2

r = -12/2

r = -6.

In conclusion, we can infer and logically deduce that each representation is matched with its respective average rate of change as follows:

h(x) ⇒ 4
f(x) ⇒ 5
g(x) ⇒ 2
j(x) ⇒ -6

Read more on rate of change here: brainly.com/question/9645290

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