|
Question 656729: have you seen people adding chlorine to their pools? this is done to reduce the number of bacteria present in the water. uppose that after t days, the number of bacteria per cubic centimetre is given by the expression B = 20t^2 - 120t + 200. in how many days will the number of bacteria be at its lowest?
Answer by ewatrrr(24785)   (Show Source):
You can put this solution on YOUR website!
Hi,
1. Read the problem.
after t days, the number of bacteria per cubic centimetre is given by the expression B = 20t^2 - 120t + 200
in how many days will the number of bacteria be at its lowest?
2. Select the unknown.
3. Translate into an equation:
Given: B = 20t^2 - 120t + 200 0r t^2 - 6t + 10
4. Use the rules to solve.
B = (t-3)^2 + 1 (found by Completing the Square)
Using the vertex form of a Parabola opening up(a>0) or down(a<0), 
where(h,k) is the vertex: V = (3,1)
5. Verify the result
By definition, V(3,1) is the low point of the "Bacteria Level" and t = 3days
B = 20t^2 - 120t + 200.
B = t^2 - 6t + 10 = (t-3)^2 - 9 + 10 = (t-3)^2 + 1
B = (t-3)^2 + 1
B represents a Parabola Opening Upward, V = (3,1)
In  days, bacteria be at its lowest
|
|
|
| |
