May 6th, 2017, 06:21 AM  #1 
Newbie Joined: Mar 2017 From: Iceland Posts: 22 Thanks: 0  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)+111,26x600 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 yaxis. 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? 
May 6th, 2017, 07:35 AM  #2  
Math Team Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416  Quote:
Quote:
 
May 6th, 2017, 08:02 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 3,261 Thanks: 894 
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. 
May 6th, 2017, 08:29 AM  #4 
Math Team Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416 
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. Last edited by skeeter; May 6th, 2017 at 08:33 AM. 
May 6th, 2017, 08:43 AM  #5 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 12,914 Thanks: 883  
May 6th, 2017, 09:35 AM  #6  
Newbie Joined: Mar 2017 From: Iceland Posts: 22 Thanks: 0  Quote:
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.  
May 6th, 2017, 09:41 AM  #7  
Math Team Joined: Jul 2011 From: Texas Posts: 2,761 Thanks: 1416  Quote:
$f\left(\dfrac{111.26}{8}\right) = 173.67... \approx 174 \, \text{customers}$  

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