Estimate the population of bacteria at 9 hours.
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

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- anonymous

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- anonymous

@xapproachesinfinity

- xapproachesinfinity

did you try drawing this!

- xapproachesinfinity

to see what kind of graph it might be

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## More answers

- anonymous

No, i don't know where to start. But i do have to show my work

- xapproachesinfinity

well look for an online plotter
put all of those points then post the picture you got here

- anonymous

ok one second

- xapproachesinfinity

this looks like a polynomial to me!

- anonymous

http://www.wolframalpha.com/input/?i=%280%2C5.1%29+%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

- mathmate

When the numbers are given in equal intervals, another way is to calculate the differences of the given numbers. If the differences are not constant, it means that the function does not represent a straight line.
However, you can calculate the differences of the previously calculated differences. If the second difference is constant, the function is a quadratic. You can then continue the sequences to find f(9).

- anonymous

How do i keep it going to find the answer for 9 hours though

- xapproachesinfinity

the second difference is constant 0.76
so it really is a quadratic

- anonymous

so how do we use the quadratic to find the answer? im confused and need to show my work

- xapproachesinfinity

there is a different method then the sequence
f(x)=ax^2+bx+c
f(0)=5.1
f(1)=3.03
f(2)=1.17
you got 3 equation in terms of a,b,c
solve for them

- xapproachesinfinity

if you got the equation
you plug 9
for f(9)

- anonymous

A=3.8 B=-2.45 and C=5.1

- xapproachesinfinity

no no

- anonymous

I had to find that in the question previous to this one

- anonymous

Are we doing it differently because we are plugging in the 9?

- xapproachesinfinity

you have to find a,b , and c plug 0 for one equation
1 for the second
2 doe the third
system of three equation

- xapproachesinfinity

f(0)=5.1=c
actually c is good!

- xapproachesinfinity

how did you find b and a

- xapproachesinfinity

f(1)=3.03=a+b
f(2)=1.72=4a+2b

- xapproachesinfinity

oh i forgot c
a+b+c=3.03
4a+2b+c=1.72

- xapproachesinfinity

c=5.1

- anonymous

Ok i've written what we have so far

- xapproachesinfinity

solve that for a and b

- anonymous

4a+2b=-3.38?

- xapproachesinfinity

yes!
now you have two equation
solve for a and b

- xapproachesinfinity

i got a=0.38
b=-2.45

- anonymous

thats what i have

- xapproachesinfinity

so we have f(x)=0.38x^2-2,45x+5.1

- xapproachesinfinity

http://prntscr.com/7odnai
looks like the shape we have before

- xapproachesinfinity

plug in 9 for f(9)

- anonymous

How do i do that though ? thats where i get lost

- xapproachesinfinity

f(9)=0.38 (9)^2-2.45(9)+5.1

- xapproachesinfinity

you just replace x by 9

- anonymous

oh ok, one sec im gonna calculate

- anonymous

F= 30.78-22.05+5.1

- xapproachesinfinity

we need final value what is it?

- anonymous

13.83

- xapproachesinfinity

yes!

- xapproachesinfinity

that's the number of bacteria after 9hours in thousands

- anonymous

So thats our final answer 13.83? :)

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