A 840 gallon pool stores water for irrigation. The water is contaminated by a to

Question

A 840 gallon pool stores water for irrigation. The water is contaminated by a toxic substance at a concentration of 80 ppm (parts per million). A filter is installed that can remove 70% of the toxin. It can filter 10 gallons per minute. The filtered water is returned to the tank and instantly mixed throughout the pool.

(a)Write a differential equation modeling the concentration x of heavy metals in the pool. Use x and t if necessary.

i.e. dx/dt=?

(b)How long will it take for the concentration to be reduced below 1 ppm? (Do not round your answer.) (in minutes)

Explanation / Answer

Initial concentration of toxin= 80*840*10^-6=0.0672 galllon

Amount of toxin in 10 gallon of water= 0.0672*10/840=8*10^-4 gallon

Amount of toxin filltered per minute=5.6*10^-4 gallon

So, dx/dt=-5.6*10^-4

       x= -5.6*10^-4t+c

       Initial concentration (at t=0) =0.0672 galllon

      c= 0.0672

So, x= -5.6*10^-4t+0.0672

For 1 ppm, concentration of heavy metal= 1*840*10^-6 =8.4*10^-4 gallon

8.5*10^-4=-5.6*10^-4t+0.0672

t=118.5 minutes

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