Question

Determining tree biomass It is easy to measure the “diameter at breast height” of a tree. It’s hard to measure the total “aboveground biomass” of a tree, because to do this you must cut and weigh the tree. The biomass is important for studies of ecology, so ecologists commonly estimate it using a power model. Combining data on $378$trees in tropical rain forests gives this relationship between biomass $y$ measured in kilograms and diameter x measured in centimeters:

$\widehat{\ln y}=-2.00+2.42\ln x$

Short answer

The biomass of a tropical tree $30$centimeters in diameter

is$\hat{y}=508.213$.

Step-by-step solution

Given Information

Given in the question that,

$\ln \hat{y}=-2.00+2.42\ln x$.

Explanation

we must calculate the biomass of a tropical tree with a diameter of $30$centimeters. As a result, we'll rate the model as follows:

$\ln \hat{y}=-2.00+2.42\ln x$

$\Rightarrow \ln \hat{y}=-2.00+2.42\ln \left(30\right)$

$\Rightarrow \ln \hat{y}=6.23090$

localid="1651133502568" $\Rightarrow \hat{y}=e^{6.23090}$

$=508.213$