Question

practice problem #1
background: the thickness of the annual rings indicates what type of environmental situation was occurring the time of the trees development. a thin ring usually indicates a rough period of development such as lack of water, forest fires, or insect infestation. on the other hand, a thick ring means a prosperous period of development. use the information from the data table below to create a proper scientific graph and to answer the corresponding questions.

age of trees (in years)	average thickness of annual rings in forest a (millimeters)	average thickness of annual rings in forest b (millimeters)
20	24	28
30	30	35
35	34	38
50	41	45
60	46	51

1. what is the dependent variable?
2. what is the independent variable?
3. what was the average thickness of annual rings for 40 - year - old trees in forest a?
4. what is it called when you make predictions within given data, such as made in question #3?
5. what was the mean thickness of annual rings for all trees found in forest b?
6. based on the data shown, what can be concluded about the comparative health of forest a & b?
7. what type of relationship (constant, direct, or indirect) exists between the age of trees and the average thickness of the trees rings? explain.

use pencil to make graph!
page 3

Explanation:

Step1: Identify dependent variable

The variable that depends on another. Here, the average thickness of annual rings depends on the age of trees. So, it is the dependent variable.

Step2: Identify independent variable

The variable that is manipulated or changed. The age of trees is being changed or considered in different values, so it is the independent variable.

Step3: Estimate for 40 - year - old trees in Forest A

Since the data has values for 35 - year - old (34 mm) and 50 - year - old (41 mm) trees in Forest A, we can estimate. The relationship seems linear. The increase from 35 - year - old to 50 - year - old is 41 - 34 = 7 mm in 15 years. So, the average increase per year is $\frac{7}{15}\approx0.47$ mm. From 35 - year - old to 40 - year - old (5 years), the increase is approximately $0.47\times5 = 2.35$ mm. So, the thickness for 40 - year - old trees is approximately 34+2.35 = 36.35 mm.

Step4: Define interpolation

Interpolation is making predictions within given data points.

Step5: Calculate mean for Forest B

The values for Forest B are 24, 28, 35, 38, 45, 51. The sum is 24 + 28+35 + 38+45 + 51=221. There are 6 data - points. The mean is $\frac{221}{6}\approx36.83$ mm.

Step6: Compare forest health

The average thickness of annual rings in Forest B is generally higher than in Forest A for the same ages, indicating that trees in Forest B may be healthier on average.

Step7: Determine relationship type

As the age of trees increases, the average thickness of the tree's rings also increases, so it is a direct relationship.

Answer:

1. Average thickness of annual rings
2. Age of trees
3. Approximately 36.35 mm
4. Interpolation
5. Approximately 36.83 mm
6. Trees in Forest B may be healthier on average as their annual - ring thicknesses are generally higher for the same ages.
7. Direct relationship. As the age of trees increases, the average thickness of the tree's rings increases.