It' s easy to measure the circumference of a tree' s trunk, but not so easy to measure its height. Foresters developed a model for ponderosa pines that they use to predict the tree' $s$ height (in feet) from the circumference of its trunk (in inches): $\ln \hat { h } = - 1.2 + 1.4 ( \ln C$ ). A lumberjack finds a tree with a circumference of $60 ^ { \prime \prime }$; how tall does this model estimate the tree to be?
A) 11 ,
B) $83 ^ { \prime }$
C) $93 ^ { \prime }$,
D) $19 ^ { \prime }$
E) 5 '

Question

Quizplus · Accepted Answer

To find the estimated height, substitute $C = 60$ into the model: $\ln \hat{h} = -1.2 + 1.4 (\ln 60)$. Calculate $\ln 60$, then multiply by 1.4, add -1.2, and exponentiate the result to find $\hat{h}$. This gives approximately 93 feet.

It' S Easy to Measure the Circumference of a Tree sss

It' S Easy to Measure the Circumference of a Tree $s$