Chapter 6, Exercises for Section 6.3, Question 14cd

The data below show the average heights of 12 Weeping Higan cherry trees planted in Washington, D.C., as they grew over time. At the time of the planting, each of the trees was one year old and 6

feet in height. A logarithmic regression model that represents the data is h = 6.1082 In x + 6.0993, where x =age of tree (in years) and h =average height of the trees (in feet).

Age of Tree

Height

(years)

(feet)

FEDON a VIA WNE

6.0

9.5

13.0

15.0

16.5

17.5

18.5

19.0

19.5

19.7

19.8

a. Use the model to predict the height of a cherry tree when it is 22 years old. How confident are you in your prediction?

Round your answer to one decimal place.

The model predicts that a 22 year old tree will have a height of

feet.

The answer seems reasonable, however, the data shows that the older the tree gets the

the height increases.

b. Using the table, estimate the age of a 16 -foot cherry tree. Then use the given regression model to calculate the average age of a 16 -foot tree.

Round your answer for the estimate using the table to one decimal place, and your answer for the estimate using the model to two decimal places.

Using the table, the average age of a 16 -foot cherry tree is about

years.