1.2 What is the Business Cycle?
By Ashton Winstead
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Last updated over 1 year ago
28 Questions
Note from the author:
Lesson Details
Experience
Over time, all economies go through regular cycles of expansion and contraction. This is called the business cycle.
Today we’ll look at a graph depicting how Gross Domestic Product (GDP) changes with respect to time.
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1.
What do you notice about this graph? What do you wonder?
What do you notice about this graph? What do you wonder?
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2.
At each of the points A, B, and C, determine if GDP is increasing or decreasing.
At each of the points A, B, and C, determine if GDP is increasing or decreasing.
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3.
The maximum and minimum values of a business cycle are called peaks and troughs.
The maximum and minimum values of a business cycle are called peaks and troughs.
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4.
What can you say about the rate of change of GDP at these peaks and troughs?
What can you say about the rate of change of GDP at these peaks and troughs?
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5.
Is GDP increasing and decreasing at a constant rate? Explain.
Is GDP increasing and decreasing at a constant rate? Explain.
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6.
At Point D, GDP is increasing. Is the growth in GDP speeding up or slowing down? How do you know?
At Point D, GDP is increasing. Is the growth in GDP speeding up or slowing down? How do you know?
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When is GDP changing the fastest? How can you tell this from the graph?
When is GDP changing the fastest? How can you tell this from the graph?
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8.
At Point E, is the slope of the curve negative or positive? What does this mean in the context of this problem?
At Point E, is the slope of the curve negative or positive? What does this mean in the context of this problem?
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9.
At Point E, are the slopes increasing or decreasing? What does this tell you about how GDP is changing at this part of the business cycle?
At Point E, are the slopes increasing or decreasing? What does this tell you about how GDP is changing at this part of the business cycle?
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10.
Describe what is happening at Point F with as much detail as possible.
Describe what is happening at Point F with as much detail as possible.
Formalize
What is concavity?
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11.
Define concavity in your own words.
Define concavity in your own words.
A function is concave up if the rate of change is increasing.
A function is concave down if the rate of change is decreasing.
A point where a function changes from concave up to concave down or vice versa is called an inflection point, or point of inflection.
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13.
Sketch a graph that meets the following requirements:
f(x) is decreasing and concave down for x<-2f(x) is decreasing and concave up for -2<x<0f(x) is increasing and concave up for 0<x<3f(x) is increasing and concave down for x>3
Sketch a graph that meets the following requirements:
f(x) is decreasing and concave down for x<-2
f(x) is decreasing and concave up for -2<x<0
f(x) is increasing and concave up for 0<x<3
f(x) is increasing and concave down for x>3
Tell me what each interval represents for the function.
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14.
0 < x < 3
0 < x < 3
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15.
(-∞,-1.5)
(-∞,-1.5)
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16.
x>3.5
x>3.5
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17.
(-1.5,1.5)
(-1.5,1.5)
Practice
The graph of a function f is shown.
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18.
Is f increasing or decreasing at x = −1? How do you know?
Is f increasing or decreasing at x = −1? How do you know?
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19.
Is the rate of change of f increasing or decreasing at x = −1? How do you know?
Is the rate of change of f increasing or decreasing at x = −1? How do you know?
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20.
Approximately on which interval of the domain is the graph of f concave down?
Approximately on which interval of the domain is the graph of f concave down?
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21.
On which interval of the domain is the graph of f concave up?
On which interval of the domain is the graph of f concave up?
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22.
Estimate the x-value of the point of inflection.
Estimate the x-value of the point of inflection.
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23.
Describe what this point tells you about how f is changing.
Describe what this point tells you about how f is changing.
Values for the rate of change of f at the 5 values given in the table below are -4.25, -3, 1, 4, and 9.75.
Fill in the table below to match each rate of change with the x-value where it occurs.
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