A contaminant is leaking into a lake at a rate of R(t) = 1200e^0.06t gallons/h. Enzymes...

A contaminant is leaking into a lake at a rate of R(t) = 1200e^0.06t gallons/h. Enzymes have been added to the lake that neutralize the contaminant over time so that after t hours the fraction that remains is S(t) = e^−0.32t. If there are currently 18,000 gallons of the contaminant in the lake, how many gallons are present in the lake 18 hours from now? (Round your answer to the nearest whole number.)

Expert Solution

Solution:

This is a differential equation problem, we have a constant flow of contaminant into the lake, but also we know that only a fraction of that quantity of contaminant remains because of the enzymes. For that reason, the differential equation of contaminant's flow into the lake would be,

when

Therefore,

milcah answered 2 years ago

A contaminant is leaking into a lake at a rate of R(t) = 1600^e0.06t gallons/h. Enzymes...

A contaminant is leaking into a lake at a rate of R(t) = 1600^e0.06t gallons/h. Enzymes have been added to the lake that neutralize the contaminant over time so that after t hours the fraction that remains is S(t) = e^−0.32t. If there are currently 19,000 gallons of the contaminant in the lake, how many gallons are present in the lake 18 hours from now? (Round your answer to the nearest whole number.)

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