Problema Solution
Paula is a peach grower in central Georgia and wants to expand her peach orchard. In her current orchard, there are 30 trees per acre and the average yield per tree is 600 peaches. Data from the local agricultural experiment station indicates that if Paula plants more than 30 trees per acre, once the trees are in production, the average yield of 600 peaches per tree will decrease by 12 peaches for each tree over 30. She needs to decide how many trees to plant in the new section of the orchard.
Is this relationship linear or nonlinear?
Answer provided by our tutors
lets assume the relationship is linear then
x = represent the number of trees planted and x > 30
if the relation ship is linear for every x, x>30 the following is valid:
30/x = 600/(600 - 12(x - 30)) cross-multiply
600x = 30(600 - 12(x - 30)) divide both sides by 30
20x = 600 - 12x + 360
20x + 12x = 960
32x = 960
x = 30
the relationship is not linear because for x different from 30 the equation 30/x = 600/(600 - 12(x - 30)) is not identity.