An element with a mass of 840 grams decays by 7% per minute. To the nearest minute, how long will it be until there are 200 grams of the element remaining?

The element takes 19.78 minutes to reach 200 grams, if an element with a mass of 840 grams decays by 7% per minute.

Step-by-step explanation:

The given is,

                  Mass of an element.

                  Decays by 7% per minute.

Step: 1

                 Formula to calculate the mass of element with an decay rate after some time period,

                                ..........................(1)

                 Where, F - Mass of element after t period

                              P - Mass of element at initial

                               r - Rate of decay of element

                               t - Time in minutes

Step: 2

                 From the give values,

                            F = 200 grams

                            P = 840 grams

                             r = 7 % per minute

                Equation (1) become,

               Take log on both sides,

                 ㏒ 0.238095 = (t) ㏒ 0.93

                   -0.6232493 = (t) (-0.03151705)

                                        =  19.77498

                                     t ≅ 19.78 minutes

Result:

              The element takes 19.78 minutes to reach 200 grams, if an element with a mass of 840 grams decays by 7% per minute.

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