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anonymous
 one year ago
In an experiment a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.
Find a quadratic model for the data in the table. Show work
anonymous
 one year ago
In an experiment a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again. Find a quadratic model for the data in the table. Show work

This Question is Closed

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Getting the table, one moment

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Time (hours) 0 1 2 3 4 5 6 Population (1000s) 5.1 3.03 1.72 1.17 1.38 2.35 4.08

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how are you supposed to do this (just asking because you have to "show work")

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I have no clue lol I typed everything the question asked and the table

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2The general formula for quadratic eqn is y = ax^2 + bx + c take any 3 points from the table (0, 5.1) (1, 3.03) (5, 2.35) plug these points into the above equation and you will get 3 different equations use substitution or any method that you know to solve these 3 eqns with 3 unknowns

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0then use a calculator http://www.wolframalpha.com/input/?i=quadratic+%280%2C5.1%29%2C%281%2C3.03%29%2C%282%2C1.72%29%2C%283%2C1.17%29%2C%284%2C1.38%29%2C%285%2C2.35%29%2C%286%2C4.08%29

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2a point is written in the form (x,y) so plug 0 for x and 5.1 for y to get 1st eqn. follow same method to get other 2 eqns

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@DecentNabeel i am not sure that would work, since it is not exact

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So this part is correct? The general formula for quadratic eqn is y = ax^2 + bx + c take any 3 points from the table (0, 5.1) (1, 3.03) (5, 2.35) plug these points into the above equation and you will get 3 different equations use substitution or any method that you know to solve these 3 eqns with 3 unknowns

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2@satellite73 many way for solve i solve another but this is true

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if it is exact you can do it using only three points \[(0,5.1),(1,3.03),(2,2.35)\] or any other 3

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0also you do not have to solve a system of three equations, only two

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0you want \[ax^2+bx+c\] but sine \((0,5.1\) is on the graph, you have \(c=5.1\) right away, only need \(a\) and \(b\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0So lets write step one so i can start writing it so i can show our work lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the part you wrote above is correct

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.25.1 = a*0^2 + b*0 + c 3.03 = a*1^2 + b*1 + c 2.35 = a*5^2 + b*5 + c solve of a, b and c

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what @DecentNabeel said solve that system but really it is not as hard as it looks since the first one tells you \(c=5.1\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0I dont know how to plug all that in

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oops second one is \[3.03=a+b=5.1\] so \[a+b=2.07\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you see how @DecentNabeel got this one \[5.1 = a*0^2 + b*0 + c\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if the answer is "no" that is fine, just say so

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2yes c=5.1 @satellite73

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok do you get that you are trying to find \(a,b\) and \(c\) to make up \[y=ax^2+bx+c\]?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok and from the table you see that \((0,5.1)\) is on the graph right?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0that means if \(x=0\) then \(y=5.1\) right ?

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2What @LynFran ????

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@satellite73 are you back? The serve kicked me off

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2@EllenJaz17 what are you said @LynFran

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0they interrupted me learning lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok so to resume our story, were were here: we want \(a,b,c\) so make \(y=ax^2+bx+c\) and we know if \(x=0\) then \(y=5.1\) plug them in and get \[5.1=a\times 0^2+b\times 0+c\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yes i get that one because its easy because x is 0 lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0right so that tells us right away that \(c=5.1\) yes?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok now \(a\) and \(b\) to go

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@LynFran send him a message, im trying to get hw help, not get interrupted

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0the next point we have is \((1,3.03)\) right ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now don't forget, we already know \(c=5.1\) so we have \[y=ax^2+bx+5.1\] put \(x=1\) and \(y=3.03\) to get \[3.03=a\times 1^2+b\times 1+5.1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0this also cleans up nicely, since \(1^2=1\) we have \[3.03=a+b+5.1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now to make it neater, subtract \(5.1\) from both sides that gives \[2.07=a+b\] or \[a+b=2.07\] and we put that aside for the moment

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0how we doing so far?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435898261868:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok now one more equation to go you can pick any point you like but i will pick \((2,1.72)\)

DecentNabeel
 one year ago
Best ResponseYou've already chosen the best response.2good @satellite73

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0again we have \[y=ax^2+bx+5.1\] put \(x=2,y=1.72\) and get \[1.72=a\times 2^2+b\times 2+5.1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now we clean it up actually you can what do you get in terms of \(a,b\) and a number ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0\[2.07^{2}+1.72+5.1\] ? Im sure that's wrong

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0quite wrong, it is much easier than that

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0haha oh jeez. I needed this class apparently very much lol and your help

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lets go back to \[1.72=a\times 2^2+b\times 2+5.1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0your equation will have an \(a\) and a \(b\) in it all you have to do is compute \(2^2\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no just \(a\times 4\) or \(4a\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lets back up a second

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0remember that when we replace \(x\) by \(1\) and \(y\) by \(3.03\) we ended up with an equation with both an \(a\) and a \(b\) in it it was \[a+b=2.07\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we are trying to accomplish the same thing here with \(x=2\) and \(y=1.72\) first step is to write \[1.72=a\times 2^2+b\times 2+5.1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so don't do too much work just see what the numbers give you your equation should still have an \(a\) and a \(b\) in it

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0if you are still confused, say so and i will spell it out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0thought so i am just going to rewrite \[1.72=a\times 2^2+b\times 2+5.1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0since \(2^24\) this is the same as \[1.72=a\times 4+b\times 2+5.1\] clear?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i meant "since \(2^2=4\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok now we just make it look better \[1.72=4a+2b+5.1\] go that ?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0again we subtract \(5.1\) from both sides and arrive finally at \[4a+2b=3.38\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now lets get those two equations together \[a+b=2.07\\ 4a+2b=3.38\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0damn \[a+b=2.07\\ 4a+2b=3.38\] thats better

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0we have to solve this "system of equations" to find \(a\) and \(b\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you know how to solve this system?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i hate decimals, at this point i would cheat, but you can do whatever you like

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0do you have to show ALL your steps?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0no it just says show work

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0well we have come this far, lets grind it out

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0probably the easiest thing to do is rewrite \[a+b=2.07\] as \[b=2.07a\] and substitute that in the second equation get \[4a+2(2.07a)=3.38\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok im just writing as you go

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0multiply out, combine like terms, work all the magic, get \[a=.33\] i will let you grind that out for yourself, but the answer is \(a=.33\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0so all thats left to find is b, than we do the equation, correct?

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0now we know that \(a=.33\) and \[a+b=2.07\] you have \[.33+b=2.07\] so \[b=2.4\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0yeah that is it , find \(a\) and \(b\) we get \(a=.33\) and \(b=2.4\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and we recall that \(c=5.1\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dang i made a mistake somewheres \(b=2.45\) actually but whatever

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0oh damn damn damn i made a stupid typo

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0everywhere you see \(.33\) replace it by \(.38\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0i told you i hate decimals when you solve \[4a+2(2.07a)=3.38\] you get \(a=.38\)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0and since \(a=.38\) we get \(b=2.45\) final answer \[y=.33x^22.45x+5.1\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0your math teacher must hate you to give you such a mess

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0at any rate, all the steps are there you can copy them down and look at them at your leisure took a while, hope you learned something

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0should it say y=.38 or y=.33 lol

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Final Answer \[\huge \color{red}{y=.38x^22.45x+5.1}\]

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0lol great thank you so much!

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435900099694:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0Do you wanna help me with another question that relates to this table lmao @satellite73

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0hell no not without a shot of tequila

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0ok post i will take a look, maybe it will be easier

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0dw:1435900241301:dw

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0good, no lime or salt (for sissies)

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0what is the question i am about to turn in to a pumpkin

anonymous
 one year ago
Best ResponseYou've already chosen the best response.0@satellite73 sorry are you still there
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