Page 51 - How To Solve Word Problems In Calculus
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EXAMPLE 12
                               An 1800-gallon tank of water drains from the bottom in
                               30 minutes. According to Torricelli’s law, the volume of
                               water remaining in the tank after t minutes is

                                                                2
                                                            t
                                            V = 1800 1 −             0 ≤ t ≤ 30
                                                           30
                               How fast is the water draining from the tank after 20 minutes?

                                   Solution



                                               dV                t       1
                                                   = 3600 1 −         −
                                               dt               30      30

                                                                 t
                                                   =−120 1 −
                                                                30
                               When t = 20

                                      dV               20
                                         =−120 1 −          =−40 gallons per minute
                                      dt               30
                               Water is draining at the rate of 40 gallons per minute. The
                               negative sign indicates that the volume of water is getting
                               smaller.


                               EXAMPLE 13
                               An environmental study of a small town indicates that in t
                                                                                          3
                               years the level of carbon monoxide will be q(t) = 0.005t +
                                    2
                               0.02t + 0.01t + 2.5 parts per million (ppm). At what rate
                               will the CO level be increasing 1 and 2 years from now?


                                   Solution
                                   The rate of change of the CO level after t years is
                                            2

                               q (t) = 0.015t + 0.04t + 0.01
                               After 1 year q (1) = 0.015 + 0.04 + 0.01 = 0.065 ppm per year

                               After 2 years q (2) = 0.06 + 0.08 + 0.01 = 0.15 ppm per year

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