Need help with Exercise 2H Question 3 Part b) (Modelling with quadratics)

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viktorschk72
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I have a problem with this question:

A fertiliser company uses a model to determine how the amount of fertiliser used, f kilograms per hectare, affects the grain yield g, measured in tonnes per hectare.

g=6+0.03f -0.00006f^2

b) One farmer currently uses 20 kilograms of fertiliser per hectare. How much more fertiliser would he need to use to increase his grain yield by 1 tonne per hectare?

Here's what I did:

g=6+0.03(20)-0.00006(20)^2
g=6.576

7.576=6+0.03f-0.00006f^2
0=(-1.576)+0.03f-0.00006f^2

and then I used the quadratic formula and got: g=47.937... but the answer sheet on the back of the book says that the answer should be 39.6 - what have I done wrong?
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mqb2766
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(Original post by viktorschk72)
I have a problem with this question:

A fertiliser company uses a model to determine how the amount of fertiliser used, f kilograms per hectare, affects the grain yield g, measured in tonnes per hectare.

g=6+0.03f -0.00006f^2

b) One farmer currently uses 20 kilograms of fertiliser per hectare. How much more fertiliser would he need to use to increase his grain yield by 1 tonne per hectare?

Here's what I did:

g=6+0.03(20)-0.00006(20)^2
g=6.576

7.576=6+0.03f-0.00006f^2
0=(-1.576)+0.03f-0.00006f^2

and then I used the quadratic formula and got: g=47.937... but the answer sheet on the back of the book says that the answer should be 39.6 - what have I done wrong?
Wolfram alpha gives 60 and 440 as the answers
https://www.wolframalpha.com/input/?...x-0.00006x%5E2
He therefore uses 40 MORE (20+39.6 = 60).
Looks like you've made a mistake on solving the quadratic, however you've done it.
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xIshaa
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why dont you use 440?
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mqb2766
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(Original post by xIshaa)
why dont you use 440?
The farmer is tight and lazy.
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xIshaa
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(Original post by mqb2766)
The farmer is tight and lazy.
Ok then 😂
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AlexAlexAlex3
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Maybe its because on the third line of your working, you typed 7.576 instead of 6.576. Its a little mistake
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