Questions: Suppose that a country's annual growth rates over a 10-year period were as follows: Year Growth Rate 1 58 2 3 3 4 4 -1 5 -2 6 3 7 4 8 5 9 6 10 2 Instructions: In part a, round your answer to 1 decimal place. In parts b-c, enter your answers as a whole number. a. What was the country's trend rate of growth over this period? percent b. Which set of years most clearly demonstrates an expansionary phase of the business cycle? Years through c. Which set of years best illustrates a recesșionary phase of the business cycle? Years through

Let's address each part of the question step by step.

To find the trend rate of growth, we need to calculate the average growth rate over the 10-year period.

The growth rates for each year are: 58, 3, 4, -1, -2, 3, 4, 5, 6, 2

First, sum these growth rates: \[ 58 + 3 + 4 - 1 - 2 + 3 + 4 + 5 + 6 + 2 = 82 \]

Next, divide the sum by the number of years (10) to find the average: \[ \text{Average growth rate} = \frac{82}{10} = 8.2 \]

So, the trend rate of growth over this period is: \[ \boxed{8.2} \text{ percent} \]

An expansionary phase of the business cycle is characterized by positive growth rates. We need to identify the longest continuous period of positive growth rates.

From the data:

• Year 1: 58
• Year 2: 3
• Year 3: 4
• Year 4: -1 (negative growth, end of expansion)
• Year 5: -2 (negative growth)
• Year 6: 3
• Year 7: 4
• Year 8: 5
• Year 9: 6
• Year 10: 2

The longest continuous period of positive growth rates is from Year 6 to Year 10.

So, the set of years that most clearly demonstrates an expansionary phase is: \[ \boxed{6} \text{ through } \boxed{10} \]

A recessionary phase of the business cycle is characterized by negative growth rates. We need to identify the longest continuous period of negative growth rates.

From the data:

• Year 1: 58
• Year 2: 3
• Year 3: 4
• Year 4: -1 (negative growth)
• Year 5: -2 (negative growth)
• Year 6: 3 (positive growth, end of recession)
• Year 7: 4
• Year 8: 5
• Year 9: 6
• Year 10: 2

The longest continuous period of negative growth rates is from Year 4 to Year 5.

So, the set of years that best illustrates a recessionary phase is: \[ \boxed{4} \text{ through } \boxed{5} \]

a. The trend rate of growth over this period is 8.2 percent. b. The set of years that most clearly demonstrates an expansionary phase is Years 6 through 10. c. The set of years that best illustrates a recessionary phase is Years 4 through 5.