Chapter 12.2, Problem 40E

To determine

To use the model in the question to estimate the biomass of a tropical tree $30$ centimeters in diameter.

Answer to Problem 40E

  $\widehat{y}=508.213$ .

Explanation of Solution

It is given in the question the model of the biomass as:

  $\ln \widehat{y}=-2.00+2.42\ln x$

Thus, we have to estimate the biomass of a tropical tree $30$ centimeters in diameter. Thus, we will evaluate the model as:

  $\begin{array}{l}\ln \widehat{y}=-2.00+2.42\ln x\\ \Rightarrow \ln \widehat{y}=-2.00+2.42\ln (30)\\ \Rightarrow \ln \widehat{y}=6.23090\\ \Rightarrow \widehat{y}={10}^{6.23090}\\ =508.213\end{array}$