   Chapter 2.3, Problem 81E

Chapter
Section
Textbook Problem

Yield of an Apple Orchard An apple orchard has an average yield of 36 bushels of apples per tree if tree density is 22 trees/acre. For each unit increase in tree density, the yield decreases by 2 bushels/tree. Letting x denote the number of trees beyond 22/acre, find a function in x that gives the yield of apples.

To determine
The function that gives the yield of the apples in the variable of x.

Explanation

Given information:

An apple orchard has an average yield of 36 bushels of apples per tree if tree density is 22 Trees/acre. For each unit increase in tree density, the yield decreases by 2 Bushels/tree.

Calculation:

Let x be the number of tress increased, then the increase of one unit of tree density becomes 22+x

For each unit increases, the yield decreases by 2 Bushels/tree, so the yield of the apple becomes (362x)Bushels/trees .

The function that represents the total yield of apples is calculated as;

f(x)=(Numberoftrees/acre)(Totalnumberof

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