Chapter 1.1, Problem 10E

(a)

To determine

To find: The range of the ring widths of Siberian pine during 1500 to 2000.

Answer to Problem 10E

The range of the ring width function is $0\le y\le 1.6$.

Explanation of Solution

In the graph of the ring widths of a Siberian pine for the period 1500 to 2000, the x-axis represents the period from 1500 to 2000 whereas the y-axis represents the ring width of trees in mm. Since the range is the set of all y-values of the graph, it is observed from the graph that the ring widths vary from 0 mm to 1.6 mm. Thus, the range of the ring width function is $0\le y\le 1.6$ or $\left[0,1.6\right]$.

(b)

To determine

The nature of the temperature of the earth; whether the graph reflect the valconic eruction during the mid-19th centuary.

Explanation of Solution

From the graph, it is observed that the earth cooled from the mid-15th century to the 17th century. In late 1700s, there seems to be a gradual increase in the temperature of the earth whereas in late 1800s there is a decrease in the temperature. Then, the temperature of the earth is increased rapidly in the mid-19th century.

Observation:

There is a deviation in the temperature in the mid-19^th century, which could have been happened due to the volcanic eruptions. Thus, it can be concluded that the graph reflects the volcanic eruption during the mid-19^th century.