One method of calculating the approximate age, in years, of a tree of a particular species is to multiply the diameter of the tree, in inches, by a constant called the growth factor for the species. The table below gives the growth factors for three species of trees.

$$\begin{array} {|l|c|} \hline \hspace{0em}\text{ Species of Tree} & \text{Growth Factor} \\ \hline \text{American elm} & 4.0 \\ \hline \text{Black walnut} & 4.5 \\ \hline \text{Cottonwood} & 2.0 \\ \hline \end{array}$$

If an american elm and a cottonwood each now have a diameter of 3 feet, which of the following will be closest to the difference, in inches, of their diameters 20 years from now?
(1 foot = 12 inches)

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We should first construct a model given the description. Below is the simplist interpretation of the description:

$$A = dk$$ $$A = \text{ Age (years)}$$ $$d = \text{ diameter (inches)}$$ $$k = \text{ growth factor}$$

The question asks us to find the diameters of the trees after 20 years. We can rearrange the equation to find $d$.

$$d=\frac{A}{k}$$

The difference in the diameters is $10-5=\boxed{5}$. Note that we excluded the current diameter of the trees in our calculation. Because they are equivalent, it does not affect our final calculation.