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May 6th, 2017, 06:21 AM   #1
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Word Problem

One shop is open from 8 to 20 every day in the week. This function describes number of customers, where x is the hours and f(x) is the number of customers. The function is:

f(x) = -4x^(2)+111,26x-600

So when are the most of the customers inside the shop and how many customer are there then?

So if you put this function in the Geogebra app it draws it

https://www.geogebra.org/apps/


There you can see that thee peek of the function is around 174 at y-axis. I think that's related to the customers.

I know the most of the customers visit the shop at or around 14:00, but I feel it very unlikely that there is 174 customers inside the shop at 14:00.

If it's from 13:00 to 14:00 it's like 3 customers per minute so that's unlikely too. So what to do with the 174 number?
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May 6th, 2017, 07:35 AM   #2
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Quote:
So if you put this function in the Geogebra app it draws it
you didn't save the graph ... link goes to a blank geogebra page

Quote:
f(x) = -4x^(2)+111,26x-600
what does the comma between 111 and 26x mean?
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May 6th, 2017, 08:02 AM   #3
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Assuming that comma is a typo and you simply mean -4x^2+ 11126x- 600 then its derivative is -8x+ 11126. Setting that equal to 0, x= 11126/8= 1390.75.

If, instead, you accidently dropped a "4", so you mean -4x^2+ 111264x- 600 then its derivative is -8x+ 111264. Setting that equal to 0, x= 111264/8= 13908, an integer.
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May 6th, 2017, 08:29 AM   #4
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maybe the comma is meant to be a decimal ? ...

$f(x) = -4x^2 + 111.26x - 600$

If so, then the maximum number of customers is about 174 at t about 14 hours. If you find this unreasonable, then the quadratic model may be in error.

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Last edited by skeeter; May 6th, 2017 at 08:33 AM.
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May 6th, 2017, 08:43 AM   #5
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Quote:
Originally Posted by afk0901 View Post
f(x) = -4x^(2)+111,26x-600
WHY use 111.26 when trying to calculate something "approximate"?!
Make it 112:
4x^2 - 112x + 600 = 0
x^2 - 28x + 150 = 0

2x - 28 = 0
x = 14
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May 6th, 2017, 09:35 AM   #6
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Quote:
Originally Posted by skeeter View Post
maybe the comma is meant to be a decimal ? ...

$f(x) = -4x^2 + 111.26x - 600$

If so, then the maximum number of customers is about 174 at t about 14 hours. If you find this unreasonable, then the quadratic model may be in error.

So according to this there is 174 people shopping when the clock is 14:00 ?

I'am I understanding this in a right manner, giving that the quadratic model is correct? and..yeah the , was a typo and meant to be a decimal.
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May 6th, 2017, 09:41 AM   #7
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Originally Posted by afk0901 View Post
So according to this there is 174 people shopping when the clock is 14:00 ?

I'am I understanding this in a right manner, giving that the quadratic model is correct? and..yeah the , was a typo and meant to be a decimal.
yes ... the actual maximum occurs at $t = \dfrac{111.26}{8} \approx 13.9 \, hrs$

$f\left(\dfrac{111.26}{8}\right) = 173.67... \approx 174 \, \text{customers}$
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