Question

practice problem #1 graphing practice 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 fire, 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) 10 20 24 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 is the average thickness of annual - rings. It varies with the age of trees.

Step2: Identify independent variable

The age of trees is not affected by the thickness of annual - rings. It is the independent variable.

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

The ages 35 and 50 are given. For Forest A, at age 35, thickness is 34 mm and at age 50, thickness is 41 mm. The change in thickness over 15 years is 41 - 34=7 mm. The rate of change is $\frac{7}{15}\approx0.47$ mm per year. From age 35 to 40 (5 years), the increase is $0.47\times5 = 2.35$ mm. So the thickness for 40 - year - old trees is $34+2.35 = 36.35$ mm.

Step4: Define prediction within data

Predicting within given data is called interpolation.

Step5: Calculate mean for Forest B

The data for Forest B is 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: Conclude forest health

Forest B generally has thicker annual rings at the same ages, indicating it may be in a more prosperous developmental state or a more favorable environment.

Step7: Determine relationship

As the age of trees increases, the average thickness of tree rings increases. So there is a direct relationship.

Answer:

1. Average thickness of annual rings
2. Age of trees
3. 36.35 mm
4. Interpolation
5. 36.83 mm
6. Forest B may be healthier as it has thicker annual - rings at the same ages.
7. Direct relationship. As the age of trees increases, the average thickness of tree rings increases.