requestbook

Step-by-step Answer
PAGE: 537SET: ExercisesPROBLEM: 1
Please look in your text book for this problem Statement

The half-life of potassium- is billion years.

a.

Find the value of and the equation of decay.

Let is a intial amount of substance, then the amount that remains after billion years can be represents the .

                                                         (Exponential decay formula)

                                 (Substitute and )

                            (Divide each side by )

                                     (Cancel common terms)

                        (Take ln on each side)

                      ()

  (Divide each side by )

                                   (Cancel common terms)

                                   (Substitute: )

                                        (Simplify)

                                      (Substitute )

Thus, the equation for the decay of potassium- is .

b.

Find the how long will take the speciman to decay to only milligrams of potassium-.

Here and milligrams of potassium-.

                                 (Substitute and )

                            (Divide each side by )

                                   (Cancel common terms)

                      (Take ln on each side)

                      ()

                   (Substitute: )

     (Divide each side by )

                         (Cancel common terms)

It will take the specimen about years to decay to only milligrams of Potassium-.

c.

Find  how many milligrams of potassium- will be left after million years.

Here milligrams of potassium- and  years.

                      (Substitute and )

                                                 (Multiply exponents)

                                            (Use caluculator: )

                                                          (Simplify)

About milligrams of Potassium- will be left after million years.

d.

Find how long will take Potassium- to decay to one eight of its original amount.

                                    (Substitute )

                               (Divide each side by )

                                      (Cancel common terms)

                         (Take ln on each side)

                             ()

              (Substitute: )

       (Divide each side by )

                                         (Cancel common terms)

It will take years to decay to one eighth of its original amount.

a. The equation for the decay of potassium- is .

b. It will take the specimen about years to decay to only milligrams of Potassium-.

c. milligrams of Potassium- will be left after million years.

d. It will take years to decay to one eighth of its original amount.



TESTIMONIALS

"I want to tell you that our students did well on the math exam and showed a marked improvement that, in my estimation, reflected the professional development the faculty received from you. THANK YOU!!!"

June Barnett

"Your site is amazing! It helped me get through Algebra."

Charles

"My daughter uses it to supplement her Algebra 1 school work. She finds it very helpful."

Dan Pease

QUESTIONS? LET US HELP.
Simply chose a support option

My status

JOIN US ON:     
mathskey.com is not affiliated with any Publisher, Book cover, Title, Author names appear for reference only