A peach tree will produce an average of 200 lbs. of fruit per year, unless it is too crowded by other trees.?

Fifty trees per acre is acceptable, but each additional tree over fifty will reduce the annual yield of each tree by 1 lb.





Write a rule for the total yield per acre whose input is the number of trees per acre.





Use the rule to find the total yield per acre if 70 trees per acre are planted.





Use the rule to find how many trees per acre should be planted to yeild 13,689 lbs. of fruit per acre.

A peach tree will produce an average of 200 lbs. of fruit per year, unless it is too crowded by other trees.?
you need to make a 'step function'


y = 200x for x%26lt;=50


and


y=(200 - (x - 50) )x


=(250 - x)x for x%26gt;=50


so the whole function is


y(x) = { 200x .............. for x%26lt;=50


..........{ (250 - x)x ........for x%26gt;50


put x=70 in the second part


gives y(70)=(250 - 70)70=12600lb


for 13689lb question note if x=50 y=10000%26lt;13689


so we need to solve the equate the 2nd part ie


(250-x)x = 13689


x^2 - 250x +13689 = 0


solve for x using the quadratic formula gives


x=81 and 169 so there are two answers,


it would obviously be easier and cheaper to maintain 81 trees than 169 though





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