decay type of question

Question

under certain water conditions, the free chlorine in a swimming pool decomposes according to the law of uninhibited decay. after shocking his pool, Ben tested the water and found that the free chlorine content was 2.5 parts per million (ppm). 24 hours later he tested again and found it to be 2.2 ppm. what will be the reading after 3 days? If Ben must shock the pool again when it reaches 1.0 ppm, how long can he wait?

Answer 1

C = present amount of chlorine

C₀ = initial amount of chlorine

k = decay constant 

t = time

 

C = C₀e^kt

 

at t=0, C = 2.5. At t=1, C = 2.2

 

2.2 = 2.5e^k

 

e^k = .88

 

k = ln .88 = -.1278

 

C(t) = 2.5e^-.1278t

 

C(3) = 2.5e^-.1278*3 = 1.70368 ppm

 

1 = 2.5e^-.1278t

 

e^-.1278t= 0.4

 

-.1278t = ln 0.4

 

t = ln 0.4/-.1278 = 7.167 days