Question

biology
graphing practice
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!

Explanation:

Step1: Identify dependent variable

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

Step2: Identify independent variable

The variable that is manipulated or changed. Tree - age is being changed to observe the thickness of annual rings, so age of trees is the independent variable.

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

Since the data for 40 - year - old trees in Forest A is not given, we can interpolate between 35 and 50 - year - old trees. The thickness for 35 - year - old trees is 41 mm and for 50 - year - old trees is 46 mm. The difference in age is $50 - 35=15$ years and the difference in thickness is $46 - 41 = 5$ mm. For a 5 - year increase from 35 years (to 40 years), the increase in thickness is $\frac{5}{15}\times5=\frac{5}{3}\approx1.67$ mm. So the thickness for 40 - year - old trees is $41+\frac{5}{3}\approx42.67$ mm.

Step4: Define interpolation

Making predictions within given data is called interpolation.

Step5: Calculate mean thickness for Forest B

Sum of thickness values for Forest B: $24 + 28+35 + 38+45+51=221$ mm. There are 6 data - points. Mean thickness $=\frac{221}{6}\approx36.83$ mm.

Step6: Analyze forest health

In general, the average thickness of annual rings in Forest B seems to be higher than in Forest A for the same age groups, indicating that on average, trees in Forest B may be healthier.

Step7: Determine relationship

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

Answer:

1. Average thickness of annual rings
2. Age of trees
3. Approximately 42.67 mm
4. Interpolation
5. Approximately 36.83 mm
6. Trees in Forest B may be healthier on average as their annual - ring thickness is generally higher for the same age groups.
7. Direct relationship. As the age of trees increases, the average thickness of the tree's rings increases.