The function  models the annual consumption of beef, in tons, in the U.S from 2000 to 2017. where  represents the number of years since 2000.

Note: For the problems below, set the window on your calculator to x: [0..18] and y: [20000..22000]
a) Use a graphing method to determine the years in which the consumtion of beef was greater that 21335 tons per year.

Write your answer in interval notation rounding to one decimal place. 


Complete the following sentence using the information from your graph.
The annual consumption of beef was above 21335 tons per year starting in year 
.
b) Use a graphing method to determine the years in which the annual consumption of beef was less than 21135 tons per year.

Write your answer in interval notation rounding to one decimal place. 


Complete the following sentence using the information from your graph.
The annual consumption of beef was below 21135 tons per year until the year

To address these problems, let's proceed step by step.

### Given:
- The function \( f(x) \) models the annual consumption of beef (in tons) in the U.S. from 2000 to 2017.
- \( x \) represents the number of years since 2000.
- The calculator window is set to:
  - \( x \): [0, 18] (corresponding to the years 2000 to 2018)
  - \( y \): [20000, 22000] (annual consumption in tons)

### Problem (a):

1. **Objective:** Determine the years when the annual consumption of beef was greater than 21,335 tons.
   
   To solve this:
   - Graph the function \( f(x) \) on your calculator.
   - Identify where \( f(x) > 21335 \) in the graph.
   - Note the interval(s) where this condition is met.

2. **Interval Notation:** 
   The answer should be provided as an interval of years (in terms of \( x \)) where the consumption was above 21,335 tons.

3. **Complete the Sentence:**
   - Based on the interval found, identify when the consumption first exceeded 21,335 tons, and note that year.

### Problem (b):

1. **Objective:** Determine the years when the annual consumption of beef was less than 21,135 tons.
   
   To solve this:
   - Graph the function \( f(x) \) again.
   - Identify where \( f(x) < 21135 \) in the graph.
   - Note the interval(s) where this condition is met.

2. **Interval Notation:**
   The answer should be provided as an interval of years (in terms of \( x \)) where the consumption was below 21,135 tons.

3. **Complete the Sentence:**
   - Based on the interval found, determine the latest year when the consumption was below 21,135 tons and use that in your answer.

### Answer Template

For **(a)**:
1. The interval where \( f(x) > 21335 \) is: \(\boxed{[a, b]}\), rounding to one decimal place.
2. **Sentence completion:**
   - "The annual consumption of beef was above 21,335 tons per year starting in year \(\boxed{2000 + a}\)."

For **(b)**:
1. The interval where \( f(x) < 21135 \) is: \(\boxed{[c, d]}\), rounding to one decimal place.
2. **Sentence completion:**
   - "The annual consumption of beef was below 21,135 tons per year until the year \(\boxed{2000 + d}\)."

### Conclusion:
Graphing the function and analyzing it based on the \( y \) thresholds (21,335 tons and 21,135 tons) will give precise intervals for \( x \). Ensure you are using the appropriate window settings on your graphing calculator.

Would you like any further details on how to graph or analyze this? Here are some follow-up questions for deeper understanding:

1. What type of function do you expect \( f(x) \) to be (linear, quadratic, etc.)?
2. Would you like a detailed explanation of how to use the graphing calculator for this problem?
3. How can interval notation help in interpreting data from graphs?
4. Do you need help converting from years since 2000 to actual calendar years?
5. Would you like an example of determining intervals from a graph?

**Tip:** When working with inequalities on a graph, look for where the function's curve crosses or touches the threshold line. This helps in identifying the exact points for interval notation.

The function models the annual consumption of beef, in tons, in the U.S from 2000 to 2017. Use a graphing method to determine the years in which the consumption of beef was greater than 21335 tons and less than 21135 tons per year.

Analyze the annual beef consumption in the U.S. from 2000 to 2017 using graphing methods. Determine the years when consumption was above 21,335 tons and below 21,135 tons. This problem covers function graphing and solving inequalities, suitable for Grades 10-12 students.

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