Question

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

Answer 1

Equation is: at^2 + bt + c = P

t = time

P = population  

t = 1, P = 3.03. 
 t = 2, P = 1.72. 
 t = 3, P = 1.17. 


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

  a = 0.38, b = -2.45, c = 5.1. 

 quadratic equation is: P = 0.38t^2 - 2.45t + 5.1