Biology worksheet on graphing practice using tree ring data to analyze environmental conditions.

Problem Analysis and Solution

The task involves analyzing data about the thickness of annual rings in two forests (Forest A and Forest B) at different ages of trees. We need to answer several questions based on the provided data and create a graph to visualize the relationship between the age of trees and the average thickness of their annual rings.

#### Step 1: Understand the Data
The data table provides:
- Age of Trees (in years): Independent variable.
- Average Thickness of Annual Rings in Forest A (mm): Dependent variable for Forest A.
- Average Thickness of Annual Rings in Forest B (mm): Dependent variable for Forest B.

#### Step 2: Answer the Questions

##### Question 1: What is the dependent variable?
- The dependent variable is the variable that changes in response to the independent variable. Here, it is the average thickness of annual rings (both for Forest A and Forest B).

Answer: Average Thickness of Annual Rings.

##### Question 2: What is the independent variable?
- The independent variable is the variable that is manipulated or changed to observe its effect on the dependent variable. Here, it is the age of trees.

Answer: Age of Trees.

##### Question 3: What was the average thickness of annual rings for 40-year-old trees in Forest A?
- The data table does not provide the exact value for 40-year-old trees. However, we can estimate it by interpolating between the values for 35 years (34 mm) and 50 years (41 mm).

Using linear interpolation:
\[
\text{Thickness at 40 years} = \text{Thickness at 35 years} + \frac{\text{Difference in thickness}}{\text{Difference in age}} \times (\text{Target age} - \text{Lower age})
\]
\[
\text{Thickness at 40 years} = 34 + \frac{41 - 34}{50 - 35} \times (40 - 35)
\]
\[
\text{Thickness at 40 years} = 34 + \frac{7}{15} \times 5 = 34 + 2.33 \approx 36.33 \, \text{mm}
\]

Answer: Approximately 36.33 mm.

##### Question 4: What is it called when you make predictions within given data, such as made in question #3?
- Making predictions within the range of given data is called interpolation.

Answer: Interpolation.

##### Question 5: What was the mean thickness of annual rings for all trees found in Forest B?
- To find the mean thickness, sum the thicknesses for all ages and divide by the number of data points.

Sum of thicknesses in Forest B:
\[
24 + 28 + 35 + 38 + 45 + 51 = 221
\]

Number of data points: 6

Mean thickness:
\[
\text{Mean} = \frac{221}{6} \approx 36.83 \, \text{mm}
\]

Answer: Approximately 36.83 mm.

##### Question 6: Based on the data shown, what can be concluded about the comparative health of Forest A & B?
- Comparing the average thicknesses of annual rings:
- Forest A: 20, 24, 30, 34, 41, 46 mm
- Forest B: 24, 28, 35, 38, 45, 51 mm

Forest B consistently has thicker annual rings than Forest A at each age. Thicker rings generally indicate better environmental conditions and healthier tree growth.

Answer: Forest B appears to be healthier than Forest A, as it has consistently thicker annual rings across all ages.

##### Question 7: What type of relationship (constant, direct, or indirect) exists between the age of trees and the average thickness of the tree’s rings? Explain.
- From the data, as the age of the trees increases, the average thickness of the annual rings also increases. This indicates a direct relationship.

Answer: Direct relationship. As the age of the trees increases, the average thickness of the annual rings also increases.

#### Step 3: Create the Graph
To create the graph:
1. Label the x-axis as "Age of Trees (in years)".
2. Label the y-axis as "Average Thickness of Annual Rings (mm)".
3. Plot two sets of data points:
- One for Forest A.
- One for Forest B.
4. Use different symbols or colors to distinguish between Forest A and Forest B.
5. Draw lines connecting the points for each forest to show the trend.

#### Final Answers
1. Dependent variable: Average Thickness of Annual Rings.
2. Independent variable: Age of Trees.
3. Average thickness for 40-year-old trees in Forest A: Approximately 36.33 mm.
4. Term for predictions within data: Interpolation.
5. Mean thickness of annual rings in Forest B: Approximately 36.83 mm.
6. Comparative health: Forest B is healthier than Forest A.
7. Type of relationship: Direct relationship.

Boxed Final Answer:
\[
\boxed{
\begin{array}{l}
1. \text{Average Thickness of Annual Rings} \\
2. \text{Age of Trees} \\
3. \text{Approximately 36.33 mm} \\
4. \text{Interpolation} \\
5. \text{Approximately 36.83 mm} \\
6. \text{Forest B is healthier than Forest A} \\
7. \text{Direct relationship}
\end{array}
}
\]