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Determining tree biomass It is easy to measure the diameter at breast height (in centimeters) of a tree. It’s hard to measure the total aboveground biomass (in kilograms) of a tree because to do this, you must cut and weigh the tree. Biomass is important for studies of ecology, so ecologists commonly estimate it using a power model. The following figure is a scatterplot of the natural logarithm of biomass against the natural logarithm of diameter at breast height (DBH) for $378$trees in tropical rain forests. The least-squares regression line for the transformed data is ${\mathrm{lny}}^{âˆ\S }=-2.00+2.42\ln {\mathrm{x}}^{âˆ\S }\widehat{\ln y}=-2.00+2.42\widehat{\ln x}$

Use this model to estimate the biomass of a tropical tree $30$cm in diameter.

Step by step solution

01

Given Information

Given data:

02

Explanation

Substituting the value of $x$:

$\ln y=-2.00+2.42\ln x$

$=-2.00+2.42\ln 30$

$=6.23090$

Using the exponential formula:

$y={10}^{\log y}$

$={10}^{6.23090}$

$=508.213$

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