Question

A swimming pool is initially shocked with chlorine to bring the chlorine concentration to 5 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 algae 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

Exponential decay is given by
y = x(1 - r)^t
where x is the starting amount (concentration)
r is the rate of decay (written as a decimal)
t = time

Answer 2

Is this a calculus or chemistry class? I can make this very in depth or not very depending.

Answer 3

it is college algebra actually.

Answer 4

should it be y=5(0.85)^x?

Answer 5

y = 5 ( 1 - .15) ^t

Answer 6

This makes sense..theres more to the question...

c. How many days will it take for the chlorine to reach a level tolerable for swimmers? How many days before bacteria and algea will start to grow and you will need to add more chlorine?

Round your answers to one decimal place.

It will take __________days for the chlorine to reach a level tolerable for swimmers.

It will take ________ days before bacteria and algea start to grow.

Answer 7

i apologize for the inconvenience

Answer 8

what was part b)

Answer 9

part be was simply to complete construct a table based on the equation we already formulated...

Answer 10

ok thanks, give a sec

Answer 11

so you want to know when is y less than 2

Answer 12

yes...it says to round to one decimal...

Answer 13

oh so it should be (6 and 1.8)

Answer 14

you know, lets solve by logs

Answer 15

can you help me on logs...hehe im not really good at that..

Answer 16

2 = 5 (.85)^t
2/5 = (.85)^t
now take logs of both sides

Answer 17

i got t=5.6

Answer 18

ln (2/5) = ln ( .85^t)
ln (2/5) = t ln (.85)

Answer 19

yes I got that

Answer 20

is t=5.6 right?

Answer 21

so after t > 5.638 , the pool is tolerable for humans

Answer 22

5.368 days

Answer 23

oku mean 5.638 or 5.368?

Answer 24

5.638, woops

Answer 25

what about for this part of the question?
It will take ________ days before bacteria and algea start to grow.

Answer 26

so by 6 days it is tolerable
, after shocking the pool

Answer 27

now we have to solve , when is y > 1 ,
so we can solve
1 = 5 (.85 ^t)

Answer 28

t=9.9 right :)

Answer 29

thank you so much i got them right...im using wiley plus and it is difficult for me...this website is great help..

Answer 30

:D

Answer 31

im done with homework thanks to your help, see you another time :) have a great week..

Answer 32

goodbye