Aswimming pool whose volume is 10,000 gal contains water that is 0.01% chlorine. starting at t = 0, city water containing0.001% chlorine is pumped into the pool at a rate of 5 gal/min. the pool water flows out at the same rate. what is thepercentage of chlorine in the pool after 1 h? when will the pool water be 0.002% chlorine?

a) The percentage of chlorine after 1 hour is 0.00973%.

b) The pool water will habe a concentration of 0.002% chlorine at 4394 minutes (or 73.24 hours).

Step-by-step explanation:

We can define as X(t) the amount of chlorine that is in the pool at time t.

Then, the rate of change of X can be written as

being Ci the concentration of chlorine of the inflow (0.001%), f_in the inflow (5 gal/min) and f_out the outflow (the same as the inflow, 5 gal/min).

When t=0, the concentration is 0.01%, so the amount of chlorine X is

Replacing in the equation, we have

The amount of chlorine for any time t is then

a) At one hour (t=60 min), the amount of chlorine is

This amount means a concentration of

b) A concentration of 0.002% of chlorine means an amount of chlorine of

Then we can calculate

option 1 is correct.

step-by-step explanation:

y varies inversely with x and constant of variation is 4

the equation will be:

y = k/x

where k =4 so,

y = 4/x

if we put values of x of option 1 in the above equation and find values of y

y = 4/-2 => y =-2

y = 4/-1 => y = -4

y = 4/1 => y = 4

y = 4/2 => y =2

so, all the values of x and y are correct.

if we put values of x given in other options and find value of y we cannot find whole table satisfying the equation.

hence option 1 is correct.