Question

water enters a pool at an increasing rate given by W(t)=1+3t gallons per minute from t=0 to t=5 minutes. Find the amount of water that has entered the pool over these five minutes.

Answer 1

The amount of water that has entered the pool over these five minutes is 42.5 gallons.

Given the rate at which water enter the pool W(t). To calculate the amount of water that has entered the pool over these five minutes, we integrate W(t) over the interval t = 0 to t = 5.

$Amount\ of \ water=\int\limits^0_5 {W(t)} \, dt \\\\\\Amount\ of \ water=\int\limits^0_5 {(1+3t)} \, dt \\\\\\Amount\ of \ water=[t+1.5t^2]_0^5\\\\\\Amount\ of \ water=42.5\ gallons$

The amount of water that has entered the pool over these five minutes is 42.5 gallons.

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