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Use the exponential decay model, A = Aoekt, to solve the following. The half-life of a certain substance is 25 years. How long will it take for a sample of this substance to decay to 76% of its original amount?

Use the exponential decay model, A = Aoekt, to solve the following. The half-life of a certain substance is 25 years. How long will it take for a sample of this substance to decay to 76% of its original amount?

Algebra and Trigonometry (6th Edition)
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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Use the exponential decay model, A = Anekt, to solve the following. The half-life of a certain substance is 25 years. How long will it take for a sample of this substance to decay to 76% of its original amount? It will take approximately (Round to one decimal place as needed.) ... for the sample of the substance to decay to 76% of its original amount.
Transcribed Image Text:Use the exponential decay model, A = Anekt, to solve the following. The half-life of a certain substance is 25 years. How long will it take for a sample of this substance to decay to 76% of its original amount? It will take approximately (Round to one decimal place as needed.) ... for the sample of the substance to decay to 76% of its original amount.
The half-life of a certain su ow long It take for a sample of 75% of its original amount? Use the exponential decay model, A = Anekt, to solve. 0.75A0 = Age Simplify the expression. Divide.both sides of the equation by A. 0.75A = A₂e-0. A = A₂e-0.0217t -0.0217t ve this -0.0217t 0.75=e=0.0217t Take the natural logarithm on both sides. MAY 2 0.75=e -0.0217t In 0.75 = In e¯ 0.0217t In 0.75= -0.0217t Simplify the right side using In e = x. To solve for t, divide both sides by -0.0217. Round the answer to one decimal place. In 0.75= -0.0217t In 0.75 -0.0217t -0.0217 -0.0217 13.3t Print Divide. view an example 2 Divide. Get more neip tv ♫ STJ A
Transcribed Image Text:The half-life of a certain su ow long It take for a sample of 75% of its original amount? Use the exponential decay model, A = Anekt, to solve. 0.75A0 = Age Simplify the expression. Divide.both sides of the equation by A. 0.75A = A₂e-0. A = A₂e-0.0217t -0.0217t ve this -0.0217t 0.75=e=0.0217t Take the natural logarithm on both sides. MAY 2 0.75=e -0.0217t In 0.75 = In e¯ 0.0217t In 0.75= -0.0217t Simplify the right side using In e = x. To solve for t, divide both sides by -0.0217. Round the answer to one decimal place. In 0.75= -0.0217t In 0.75 -0.0217t -0.0217 -0.0217 13.3t Print Divide. view an example 2 Divide. Get more neip tv ♫ STJ A
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