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 $60 "$; how tall does this model estimate the tree to be?
A) 11'
B) $83 ^ { \prime }$
C) $93 ^ { \prime }$
D) 19'
E) $5 ^ { \prime }$

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's Trunk ln⁡h^=−1.2+1.4(ln⁡C\ln \hat { h } = - 1.2 + 1.4 ( \ln Clnh^=−1.2+1.4(lnC

It's Easy to Measure the Circumference of a Tree's Trunk $\ln \hat { h } = - 1.2 + 1.4 ( \ln C$