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

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?
Reply 1
Avatar for mqb2766
mqb2766
21
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/?i=solve+0%3D(-1.576)%2B0.03x-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.
Reply 2
Avatar for xIshaa
xIshaa
8
why dont you use 440?
Reply 3
Avatar for mqb2766
mqb2766
21
Original post by xIshaa
why dont you use 440?

The farmer is tight and lazy.
Reply 4
Avatar for xIshaa
xIshaa
8
Original post by mqb2766
The farmer is tight and lazy.

Ok then 😂
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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