An apple orchard has an average yield of 38 bushels of apples/tree if the density is 24 trees/acre. For each unit increase in tree density, the yield decreases by 2 bushels. Letting x denote the number of trees beyond 24/acre, find a function in x that gives the yield of apples

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To find the function that gives the yield of apples, we need to establish the relationship between tree density and apple yield based on the given information.

We know that the orchard has an average yield of 38 bushels of apples per tree when the density is 24 trees per acre. We also know that for each unit increase in tree density beyond 24 trees per acre, the yield decreases by 2 bushels.

Let's break it down step by step:

1. Determine the base yield: Since the average yield is 38 bushels per tree when the density is 24 trees per acre, we can calculate the base yield by multiplying the average yield per tree by the number of trees per acre:
Base Yield = 38 bushels/tree × 24 trees/acre

2. Define the equation for yield decrease: We are told that for each unit increase in tree density beyond 24/acre, the yield decreases by 2 bushels. So, for x trees beyond 24/acre, the decrease in yield can be expressed as:
Yield Decrease = 2 bushels/tree × x (trees/acre)

3. Determine the yield function: To find the yield function, we subtract the yield decrease from the base yield:
Yield = Base Yield - Yield Decrease

Substituting the values we calculated in steps 1 and 2, we get:
Yield = (38 bushels/tree × 24 trees/acre) - (2 bushels/tree × x trees/acre)

Simplifying the expression yields:
Yield = 912 bushels/acre - 2x bushels/acre

Therefore, the function that gives the yield of apples is:
Yield = 912 - 2x bushels/acre, where x represents the number of trees beyond 24/acre.