Answer: a) A quadratic model for the data in the table:\(0.38x^2-2.45x+5.1\).
b) The population of bacteria at 9 hours will be 138,30
Explanation:
a) General quadratic model formula :\(y=Ax^2+Bx+C\)
By using data given we will have three quadratic equation:
(time:population):(x,y):(0, 5.1) , (1, 3.03) , (2, 1.72)
\(5.1=A(0)^2+B(0)+C\)...(1)
\(3.03=A(1)^2+B(1)+C\)...(2)
\(1.72=A(2)^2+B(2)+C\)....(3)
On solving these equation we get value of constant A B and C:
A = 0.38 , B = -2.45 and C = 5.1
A quadratic model for the data in the table:\(0.38x^2-2.45x+5.1\)
b) The population of bacteria at 9 hours
Using the Quadratic equation determined above:
\(0.38x^2-2.45x+5.1\)
putting x = 9 hours
we get :
\(0.38(9)^2-2.45(9)+5.1\) = 13.38
Since the data of population given is in thousands so the population of the bacteria at 9 hour will be 13,830.
The population of bacteria at 9 hours will be 138,30
