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
signment page n x + 6.0993, where x =age of tree (in years) and / =average height of the trees (in feet).
Age of Tree
Height
(years)
(feet)
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 20 years old. How confident are you in your prediction?
Round your answer to one decimal place.
The model predicts that a 20 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 14 -foot cherry tree. Then use the given regression model to calculate the average age of a 14 -foot
tree.