Question

A swimming pool is initially shocked with chlorine to bring the chlorine concentration to 6 ppm (parts per million). Chlorine dissipates in reaction to bacteria and sun at a rate of about 15% per day. Above a chlorine concentration of 2 ppm, swimmers experience burning eyes, and below a concentration of 1 ppm, bacteria and algea start to proliferate in the pool environment.

a. Construct an exponential decay function that describes the chlorine concentration (in parts per million) over time.

Answer 1

Let C be the chlorine concentration in parts per million, and let Co be the initial Chlorine concentration in parts per million. We can write:

`C=C _(0)(0.85)^(t)`
where t is the time in days after the pool treatment.
Plugging in the initial value of Cl concentration gives:

`C=6(0.85)^(t)`