Question

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 630 pounds of strawberries when 70 cubic feet of fertilizer are applied. If 100 cubic of feet of fertilizer are applied, the yield will be 900 pounds of strawberries. Use linear interpolation to estimate the yield if 73 cubic feet of fertilizer are applied.

Answer 1

657 pounds

Explanation:

Given

Represent the amount of fertilizer with x and the yield with y.

So, we have:

`(x_1,y_1) = (70,630)`

`(x_2,y_2) = (100,900)`

Required:

Determine the yield (y) when fertilizer (x) is 73ft^3

Using linear interpolation, we have:

`y = y_1 + (x - x_1)((y_2 - y_1))/((x_2 - x_1))`

Substitute the x and y values using

`(x_1,y_1) = (70,630)` and
`(x_2,y_2) = (100,900)`;

We have:

`y = y_1 + (x - x_1)((y_2 - y_1))/((x_2 - x_1))`

`y = 630 + (x - 70)((900 - 630))/((100 - 70))`

`y = 630 + (x - 70)(270)/(30)`

`y = 630 + (x - 70)*9`

Open bracket

`y = 630 + 9x - 630`

`y = 9x - 630+630`

`y = 9x`

To solve for y when x = 73.

We simply substitute 73 for x

`y = 9x`

`y = 9 * 73`

`y = 657`

Hence, the yield for 73 cubic feet is 657 pounds