Question

A swimming pool is treated periodically to control harmful bacteria growth.
The concentration of bacterial per cm³ after t days is given by
C(t)
$= 30t^2 -240t + 500$
in how many days after a treatment will be concentration be minimal ?
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Answer 1

Answer:

The answer is 4

Step-by-step explanation:

$c \: (t) = {30ft}^{2} = - 240t + 500$

For a quadratic function as given to find the minimum you need to write it in vertex or find the vertex (the vertex in a quadratic function is thr maximum or minimum).

Use the next formula to find the t coordinate of the vertex (the time in the minimum concentration of bateria):

$c \: (t) = {at}^{2} + bt + c \\ \\ tm = - \frac{b}{2a}$

For the given function:

$tm = - \frac{ - 240}{(2)30} = \frac{240}{60} = 4$

The minimum concentration of bacteria will be after 4 days.