GATE 2018 CE (CE1) – Question 59
Ponded infiltration rate is $f=30+10e^{-2t}$ mm/h, with t in hours. Infiltration depth during the last 20 minutes of a 30-minute storm, to one decimal, is ______ mm.
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Correct answer: 11.0 to 12.0
Explanation
The last 20 minutes run from $t=1/6$ to $t=1/2$ hour. Integrate: $$F=\left[30t-5e^{-2t}\right]_{1/6}^{1/2}=10+5(e^{-1/3}-e^{-1})=11.7433\ \mathrm{mm}.$$ Rounded answer: 11.7 mm.