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 and use it to estimate the population of bateria at 9 hours.

Question

arihangdu · Answer

Please  help me to solve the problems.

arihangdu · Answer

With step by step instructions.

anonymous · Answer

Let the equation be : at^2 + bt + c = P, where t = time (hrs), P = population (1000's). 

When t = 1, P = 3.03. 
When t = 2, P = 1.72. 
When t = 3, P = 1.17. 

Substitute these into the equation to obtain these 3 simultaneous equations : 

a + b + c = 3.03 
4a + 2b + c = 1.72 
9a + 3b = c = 1.17 

Solving gives : a = 0.38, b = -2.45, c = 5.1. 

The equation is therefore, P = 0.38t^2 - 2.45t + 5.1 

Testing with t = 0 to 6 gives the population values as provided, 
so it seems to be a valid model. 

At t = 9 hrs, P = 0.38*9^2 - 2.45*9 + 5.1 = 13.83.

arihangdu · Answer

How you get the solving directly ?

anonymous · Answer

#ilovegoogle

arihangdu · Answer

I know that much from google but I need steps as well

anonymous · Answer

Okay give me a second

arihangdu · Answer

Alright go head

arihangdu · Answer

How to solve this with steps by steps please help me will get madels and fan