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.

Answer 1

I know the formula but i cant figure it out it makes no sense I've done
at^2+bt+c=p
t=1 p=3.03
t=2 p=1.72
t=3 p=1.17

a(1)^2+b(1)+c=3.03
a+b+c=3.03
a(2)^2+b(2)+c=1.72
4a+2b+c=1.72
a(3)^2+b(3)+c=1.17
9a+3b+c=1.17

I dont know wwhat to do from here. please help :)

Answer 2

You are being asked to fit a model of the form
\[y = a _{0} + a_{1}x + a_{2}x ^{2}\]
We say that y is a linear function of the parameters \[a _{0}, a _{1} and a _{2} \]
even though it is a quadratic function of \[x.\] Therefore we can use linear regression to fit this model.

If this is gibberish now is the time to say so and I'll offer a different approach.

Answer 3

Here's the other way after all. It assumes that the data points are error free (which is rare in real experimental situations). Notice that I chose only three of the seven points to work with. It's possible that, if I had chosen three others the answer would be slightly different once the equations are solved. The method above does not have this defect.

If I try to solve those equations my arithmetic will be wrong.