Landfill

Calculus Level pending

At the beginning of 2010, a landfill had 1400 tons of solid waste. The increasing function W W models the total amount of solid waste stored at the landfill. Planners estimate that W W will satisfy the differential equation d W d t = ( W − 300 ) 25 \dfrac{dW}{dt} = \dfrac{(W-300)}{25} for the next 20 years. W W is measured in years from the start of 2010. What will be the amount of waste when t = 1 t= 1 year?


The answer is 1444.89185.

Tasneem Khaled by Tasneem Khaled , 26, Bangladesh

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1 solution

Tasneem Khaled
Aug 10, 2017

d W d t \frac{dW}{dt} = ( W − 300 ) 25 \frac{(W-300)}{25}

or, d W W − 300 \frac{dW}{W-300} = 1 25 \frac{1}{25}

or, ∫ d W W − 300 \frac{dW}{W-300} = ∫ d t 25 \frac{dt}{25}

or C1 + ln I W - 300 I = t 25 \frac{t}{25} + C2

or, W-300 = 1100e^t/25

When t = 1 we get the answer

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