The radioactive isotope Uranium-235, used for nuclear power, has a half-life of 704 million years. Assume an initial amount of 1.8 kg. Use the the formula A(t) = Aoekt to model the situation, where Ao is the initial amount of the material and k is a constant representing the rate of decay per million years. a) Find the exact value of k, the decay constant. Round to 6 decimal places or enter an exact answer. k = b) Using the k value from part (a), find a function that gives the amount of the isotope A that remains after t million years. A(t) = c) How long will it take for 70% of the material to decay? Round to the nearest tenth of a year. (HINT: If 70% of the material decays, how much is left?)
The radioactive isotope Uranium-235, used for nuclear power, has a half-life of 704 million years. Assume an initial amount of 1.8 kg. Use the the formula A(t) = Aoekt to model the situation, where Ao is the initial amount of the material and k is a constant representing the rate of decay per million years. a) Find the exact value of k, the decay constant. Round to 6 decimal places or enter an exact answer. k = b) Using the k value from part (a), find a function that gives the amount of the isotope A that remains after t million years. A(t) = c) How long will it take for 70% of the material to decay? Round to the nearest tenth of a year. (HINT: If 70% of the material decays, how much is left?)
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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Transcribed Image Text:The radioactive isotope Uranium-235, used for nuclear power, has a half-life of 704 million years. Assume
an initial amount of 1.8 kg. Use the the formula A(t) = Aŋekt to model the situation, where Ao is the
initial amount of the material and k is a constant representing the rate of decay per million years.
a) Find the exact value of k, the decay constant. Round to 6 decimal places or enter an exact answer.
k =
b) Using the k value from part (a), find a function that gives the amount of the isotope A that remains
after t million years.
A(t):
=
c) How long will it take for 70 % of the material to decay? Round to the nearest tenth of a year.
(HINT: If 70% of the material decays, how much is left?)
Time:
million years
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