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)
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!

Explanation:

Step1: Identify dependent variable

The variable that depends on another is the average thickness of annual rings.

Step2: Identify independent variable

The variable that is manipulated or changed is the age of trees.

Step3: Find thickness for 40 - year - old trees in Forest A

From the table, for 40 - year - old trees in Forest A, the average thickness is 34 millimeters.

Step4: Define prediction within data

Predicting within given data is called interpolation.

Step5: Calculate mean for Forest B

Sum of thicknesses in Forest B: \(24 + 28+35 + 38+45+51=221\). There are 6 data - points. Mean \(=\frac{221}{6}\approx36.83\) millimeters.

Step6: Compare forest health

The average thickness of annual rings in Forest B is generally higher than in Forest A at the same ages, so Forest B may be healthier.

Step7: Determine relationship

As the age of trees increases, the average thickness of tree rings increases, so it is a direct relationship because both variables move in the same direction.

Answer:

1. Average thickness of annual rings
2. Age of trees
3. 34 millimeters
4. Interpolation
5. Approximately 36.83 millimeters
6. Forest B may be healthier as its trees generally have thicker annual rings at the same ages.
7. Direct relationship. As age increases, thickness increases.