Answer:
We can express the yield per tree as
[tex]y=-6x+780[/tex]
where y: yield per tree and x: number of trees, with x>75.
Step-by-step explanation:
With this data we have that:
1) The annual yield per lemon tree is 330 pounds per tree when the number of trees per acre is 75
[tex]y(75)=330[/tex]
being y the yield per tree.
2) For each additional tree over 75, the annual yield per tree for all trees on the acre decreases by 6 pounds
[tex]\frac{dy}{dx}=-6[/tex]
being x the number of trees.
If we rearrange and integrate we have
[tex]dy=-6dx\\\\\int dy=-6\int dx\\\\y=-6x+C[/tex]
If we use [tex]y(75)=330[/tex], we have
[tex]330=-6(75)+C=-450+C\\\\C=330+450=780[/tex]
Then we can express the yield per tree as
[tex]y=-6x+780[/tex]
