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1 the mean life of a radioactive nucleus. Show that 95% of the k Physicists using the radioactivity equation y = yo e - kt call the number 3 Thus, the mean life of a k radioactive nuclei originally present in a sample will disintegrate within three mean lifetimes, i.e., by time t = nucleus gives a quick way to estimate how long the radioactivity of a sample will last. ..... If 95% of a sample has decayed, there is 5% remaining. How can you use the radioactivity equation y(t) = yo e - kt to find when 5% of the sample is remaining? A. Set y(t) equal to 0.05 and solve for t. B. Evaluate y(0.05). O C. Set y(t) equal to 0.05yo and solve for t. O D. Evaluate y(5). Perform the operation determined in the previous step. Yo e - kt 0.05yo %3D kt = 0.05 Divide both sides by yo: = In 0.05 Take the natural logarithm of each side. In 0.05 t = Solve for t. Approximate In 0.05. In 0.05 z (Round to three decimal places as needed.) Since this value is approximately equal to 3 then 95% of a sample will disintegrate with a time of t = (Round to the nearest integer as needed.)

1 the mean life of a radioactive nucleus. Show that 95% of the k Physicists using the radioactivity equation y = yo e - kt call the number 3 Thus, the mean life of a k radioactive nuclei originally present in a sample will disintegrate within three mean lifetimes, i.e., by time t = nucleus gives a quick way to estimate how long the radioactivity of a sample will last. ..... If 95% of a sample has decayed, there is 5% remaining. How can you use the radioactivity equation y(t) = yo e - kt to find when 5% of the sample is remaining? A. Set y(t) equal to 0.05 and solve for t. B. Evaluate y(0.05). O C. Set y(t) equal to 0.05yo and solve for t. O D. Evaluate y(5). Perform the operation determined in the previous step. Yo e - kt 0.05yo %3D kt = 0.05 Divide both sides by yo: = In 0.05 Take the natural logarithm of each side. In 0.05 t = Solve for t. Approximate In 0.05. In 0.05 z (Round to three decimal places as needed.) Since this value is approximately equal to 3 then 95% of a sample will disintegrate with a time of t = (Round to the nearest integer as needed.)

Calculus: Early Transcendentals
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Physicists using the radioactivity equation y = yo e - kt call the number 1 the mean life of a radioactive nucleus. Show that 95% of the radioactive nuclei originally present in a sample will disintegrate within three mean lifetimes, i.e., by time t=. Thus, the mean life of a k nucleus gives a quick way to estimate how long the radioactivity of a sample will last. ..... - kt If 95% of a sample has decayed, there is 5% remaining. How can you use the radioactivity equation y(t) = yo e to find when 5% of the sample is remaining? A. Set y(t) equal to 0.05 and solve for t. B. Evaluate y(0.05). C. Set y(t) equal to 0.05y, and solve for t. D. Evaluate y(5). Perform the operation determined in the previous step. Yo e - kt 0.05yo - kt e = 0.05 Divide both sides by yo: = In 0.05 Take the natural logarithm of each side. In 0.05 t = Solve for t. Approximate In 0.05. In 0.05 x (Round to three decimal places as needed.) Since this value is approximately equal to then 95% of a sample will disintegrate with a time of t= (Round to the nearest integer as needed.)
Transcribed Image Text:Physicists using the radioactivity equation y = yo e - kt call the number 1 the mean life of a radioactive nucleus. Show that 95% of the radioactive nuclei originally present in a sample will disintegrate within three mean lifetimes, i.e., by time t=. Thus, the mean life of a k nucleus gives a quick way to estimate how long the radioactivity of a sample will last. ..... - kt If 95% of a sample has decayed, there is 5% remaining. How can you use the radioactivity equation y(t) = yo e to find when 5% of the sample is remaining? A. Set y(t) equal to 0.05 and solve for t. B. Evaluate y(0.05). C. Set y(t) equal to 0.05y, and solve for t. D. Evaluate y(5). Perform the operation determined in the previous step. Yo e - kt 0.05yo - kt e = 0.05 Divide both sides by yo: = In 0.05 Take the natural logarithm of each side. In 0.05 t = Solve for t. Approximate In 0.05. In 0.05 x (Round to three decimal places as needed.) Since this value is approximately equal to then 95% of a sample will disintegrate with a time of t= (Round to the nearest integer as needed.)
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