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Improper Integrals
11. Techniques of Integration / Improper Integrals / Problem 5
Problem 5

A country's water consumption rate is modeled by w(t)=w0eqt w(t) = w_0 e^{-qt} , where q>0 q > 0 , w0=2×108 w_0 = 2 \(\times\) 10^8 L/yr\(\text{L/yr}\), and the total water reserve is 8×1010 8 \(\times\) 10^{10} L\(\text{L}\). Find the minimum decay constant q q so that the water reserve lasts indefinitely.