Water is pumped into a tank at a rate of \(r(t)=10\left(1-e^{-0.33t}\right)\) gallons per minute, where \(t\) is the number of minutes since the pump was turned on. If the tank contained 100 gallons of water when the pump was turned on, how much water, to the nearest gallon, is in the tank after 15 minutes?

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The water in the tank is given by:

$$ 100 + \int \limits_0^{15} r(t)   dt $$

Using our calculator to evaluate the definite integral:

$$ \approx 100 + 42 $$ $$ = \boxed{142} $$