Question

12. In an experiment, a petri dish with a colony of bacteria is exposed to cold temperatures and then warmed again.

Time (hours) 0 1 2 3 4 5 6
Population (1000s) 5.1 3.03 1.72 1.17 1.38 2.35 4.08


a. Find a quadratic model for the data in the table. Type your answer below.
o


b. Use the model to estimate the population of bacteria at 9 hours. Type your answer below.

Answer 1

\( \begin {cases} 0a+0b+c=5.1\\
1a+1b+c=3.03\\
2^2a+2b+c=1.72 \end{cases}\)

Solve this system of equations for a, b and c.

Then your answer will be in the form of \(y=a^2x+bx+c\)

Answer 2

i mean \(y=ax^2+bx+c\)

Answer 3

I have to think about this cause I'm not very good in equations like this...

Answer 4

ok im super confused and I can't figure this out can you help me ...

Answer 5

sure, what's the problem?

Answer 6

aren't the equations to help find the y=ax^2+bx+c right? Cause if that's so I am not really sure how to do that. Also wouldn't it be easier to take the population and find the difference between the first two and continuing on through the list to find the population for hour 9?

Answer 7

That will not work because it's not a linear equation.

Answer 8

Oh ok that would make sense ... so in order to find the population then finding y=ax^2+bx+c is going to be difficult for me... I'm very confused about how to get there..

Answer 9

do you know how to solve equations like 2y+4x=7 and -3y+x=2?

Answer 10

system of equations*

Answer 11

No I had notes on it but I can't find them..

Answer 12

Hmm, alright, because that's what we need to do here.

Answer 13

Ok

Answer 14

Anyway, this one isn't particularly hard, luckily

Answer 15

The first equation is simply 0a+0b+c=5.1 Since the a and b are both multiplied by 0, they can be ignored. So it basically just sais c=5.1

Answer 16

you get that?

Answer 17

Yes

Answer 18

ok, now then let's substitude everywhere where there is a c for 5.1, since we know c=5.1

\(\begin {cases} \\
1a+1b+\color{red}{5.1}=3.03\\
2^2a+2b+\color{red}{5.1}=1.72 \end{cases}\)

Answer 19

So from that we can conclude a+b+5.1=3.03 while 4a+2b+5.1=1.72 or, if we move the numbers to one side

\( \begin {cases} \\
1a+1b=3.03- \color{red}{5.1} \\
2^2a+2b=1.72-\color{red}{5.1} \end{cases} \)

makes

\( \begin {cases} \\
1a+1b=-2.07 \\
2^2a+2b=3.83 \end{cases} \)

Answer 20

\( \begin {cases} \\
1a+1b=-2.07 \\
2^2a+2b=-3.83 \end{cases}\)

Answer 21

Ok so then we figure out what b is?

Answer 22

\( \begin{array} 22a+2b=-4.14\\
4a+2b=-3.83~-\\
\hline\\
-2a+0= -0.31\end{array}
\)

Answer 23

where did the -4.14 come from?

Answer 24

multiplying the first equation by 2

Answer 25

oh ok continue XD

Answer 26

it seems that i have made a mistake somewhere though as i don't get the answer t should give

Answer 27

And that mistake would be where?

Answer 28

thats what i'm trying to figure out

Answer 29

Do you think that -3.83 should've been doubled aswell??

Answer 30

oh no wait nvm >.<

Answer 31

this is strange.

Answer 32

maybe

Answer 33

@zimmah what was the answer to my question

Answer 34

I made a mistake with the c, let's do it again

Answer 35

\( \begin {cases} \\
1a+1b+\color{red}{5.1}=3.03\\
2^2a+2b+\color{red}{5.1}=1.72 \end{cases} \)

let's work from here.

Answer 36

I think it was when 1.72 -5.1

Answer 37

Because I did it and got -4.62

Answer 38

HEY !!!!!!!!@zimmah WHAT WAS IT

Answer 39

Edge, not now

Answer 40

what was the answer

Answer 41

haven't gotten one yet

Answer 42

\(\begin{array} 22a+2b+10.2=6.06\\
4a+2b+5.1=1.72~-\\
\hline\\
-2a+5.1= 4.34\end{array}\)

Answer 43

so -2a=4.34-5.1

\[a=-\frac{ 4.34+c }{ 2 }=0.38\]

Answer 44

and since a+b+c=3.03 we can fill it in to know 0.38+b+5.1=3.03 so b is -2.45

Answer 45

sorry for the confusion earlier, i must have messed up with subtracting with the 5.1 somewhere.

Answer 46

you did x3 and its ok we all make mistakes

Answer 47

Ok and could hint on how to find population for hour 9 ??

Answer 48

just plug in 9 for x in the formula you just created with your a, b and c

Answer 49

oh ok :3 thank you !

Answer 50

I really appreciate the help Zim :D

Answer 51

so my population number for hour 9 would be 13.83?

Answer 52

@DecentNabeel Maiṁ tumasē pyāra karatā hūm̐. Gus'sā na karēṁ.