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


a. Find a quadratic model for the data in the table. Type your answer below.

b. Use the model to estimate the population of bacteria at 9 hours. Type your answer below.

Answer 1

a) The equation is, P = 0.38 t^2 - 2.45 t + 5.1
Where,
t = time (hrs)
P = population (1000's).

b) At, t = 9 hours
P = 0.38*9^2 - 2.45*9 + 5.1
P = 13.83.

Answer 2

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

Step-by-step 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