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A radioactive element decays according to the function Q = Qoert, where Q is the amount of the substance at time t = 0, r is the continuous compound rate of decay, t is the time in years, and Q is the amount of the substance at time t. If the continuous compound rate of the element per year is r= -0.000346, how long will it take a certain amount of this element to decay to half the original amount? (The period is the half-life of the substance.) The half-life of the element is approximately years. (Do not round until the final answer. Then round to the nearest year as needed.).

A radioactive element decays according to the function Q = Qoert, where Q is the amount of the substance at time t = 0, r is the continuous compound rate of decay, t is the time in years, and Q is the amount of the substance at time t. If the continuous compound rate of the element per year is r= -0.000346, how long will it take a certain amount of this element to decay to half the original amount? (The period is the half-life of the substance.) The half-life of the element is approximately years. (Do not round until the final answer. Then round to the nearest year as needed.).

Advanced Engineering Mathematics
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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A radioactive element decays according to the function Q = Qoet, where Qo is the amount of the substance at time t = 0, r is the continuous compound rate of decay, t is the time in years, and Q is the amount of the substance at time t. If the continuous compound rate of the element per year is r = -0.000346, how long will it take a certain amount of this element to decay to half the original amount? (The period is the half-life of the substance.) The half-life of the element is approximately years. (Do not round until the final answer. Then round to the nearest year as needed.).
Transcribed Image Text:A radioactive element decays according to the function Q = Qoet, where Qo is the amount of the substance at time t = 0, r is the continuous compound rate of decay, t is the time in years, and Q is the amount of the substance at time t. If the continuous compound rate of the element per year is r = -0.000346, how long will it take a certain amount of this element to decay to half the original amount? (The period is the half-life of the substance.) The half-life of the element is approximately years. (Do not round until the final answer. Then round to the nearest year as needed.).
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