Explanation Given: Original amount 21, Half − Life in years = 152 years; Number of years = 500. Concept Used: Half − Life: The half − life of a radioactive substance is a characteristic constant. It measures the time it takes for a given amount of the substance to become reduced by half as a consequence of decay, and therefore, the emission of radiation. Symbol of Half life is t 1 / 2 Calculation: Let`s calculate x, the number of time intervals. x = 500 ( years) 152 ( half - life ) = 3.3 Now, using our exponential decay formula and the definition of half − life, for each time interval x, the decay rate r is 1 2 or 50 % or 0.50 . Exponential Decay Formula: y = C ( 1 − r ) x ; Where C is the original amount , r is the decay rate and x is the time intervals. Here: C = 21; r = 0.50; x = 3.3 y = C ( 1 − r ) x y = 21 ( 1 − 0

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ISBN: 9780135757987

Author: Martin-Gay

Publisher: PEARSON CO

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Chapter 19.4, Problem 23ES

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Find the final amount after x time intervals.

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EP ALGEBRA FOUND.:PREALG.-MYLABMATH ACC

Ch. 19.1 - Prob. 1VRVC Ch. 19.1 - Prob. 2VRVC Ch. 19.1 - Prob. 3VRVC Ch. 19.1 - Prob. 4VRVC Ch. 19.1 - Prob. 5VRVC Ch. 19.1 - Prob. 6VRVC Ch. 19.1 - Prob. 1ES Ch. 19.1 - Prob. 2ES Ch. 19.1 - Prob. 3ES Ch. 19.1 - Prob. 4ES

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Find the final amount after x time intervals.

Solution Summary: The author calculates the final amount after x time intervals using the exponential decay formula and the definition of half life.

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