A swimming pool is treated periodically to control harmful bacteria growth. The concentration of the bacteria per cm^3 after t days is given by (t)=30t^2-240t+500. In how many days after a treatment will the concentration be minimal?
To find the minimum concentration of bacteria, we need to find the minimum point of the function C(t) = 30t^2 - 240t + 500. This can be done using calculus by finding the derivative of the function and setting it equal to zero:
C'(t) = 60t - 240 = 0
Solving for t, we get t = 4.
Therefore, the concentration of bacteria will be minimal after 4 days.