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The yield of strawberry plants depends on the amount of fertilizer fed to the plants. Agricultural research shows that an acre of strawberry plants will yield 770 pounds of strawberries when 70 cubic feet of fertilizer are applied. If 100 cubic of feet of fertilizer are applied, the yield will be 1100 pounds of strawberries. Use linear interpolation to estimate the yield if 75 cubic feet of fertilizer are applied. Select an answer

Respuesta :

Answer:

825 pounds

Step-by-step explanation:

Given:

x be the cubic feet of fertilizer applied

and, y be the yield

Thus,

at x₁ = 70 cubic feet ; y₁ = 770 pounds

at x₂ = 100 cubic feet ; y₂ = 1100 pounds

now,

slope = [tex]\frac{y_2-y_1}{x_2-x_1}[/tex]

or

slope = [tex]\frac{1100-770}{100-70}[/tex]

or

slope = 11

now,

comparing with the standard equation for line i.e y = mx + c, we get

y = 11x + c

where, c is the constant

or

770 = 11 × 70 + c

or

c = 0

thus,

the relation comes as:

y = 11x

hence,

for x = 75 cubic feet

yield, y = 75 × 11 = 825 pounds

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