Whoever just answered this question did an awful job, please only answer if you

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Whoever just answered this question did an awful job, please only answer if you know what you are doing. I don't want the wrong answer, i have that already thanks

(1 point) A 960 gallon pool stores water for irrigation. The water is contaminated by a toxic substance at a concentration of 120 ppm (parts per million). A filter is installed that can remove 90% of the toxin. It can filter 10 gallons per minute. The filtered water is returned to the tank and instantly mixed throughout the pool. of heavy metals in the pool. Use x and t if necessary (a) Write a differential equation modeling the concentration dx dt (b) How long will it take for the concentration to be reduced below 1 ppm? (Do not round your answer.) The concentration will fall below 1 ppm after minutes.

Explanation / Answer

x(0)=120 ppm

dx/dt=-(x/960)10*dt+(x/960)10*0.9dt

dx/dt=-(x/960)dt

dx/x=-dt/960
ln(x)=-t/960 +C

x=A e^{-t/960}

x(0)=120 , hence, A=120

x=120 e^{-t/920}

b)

x=1=120 e^{-t/920}

Solving gives

t~4404.5 minutes

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