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3. A certain radioactive green substance has a half life of 25 years. We know that the quantity of something with radioactive decay has a formula given by P(t) = Poet, where Po is the initial quantity and k is some constant. (a) Determine k for this given substance. (b) How much time elapses before there is less than 10% of the original amount of the substance present? (c) How much time elapses before the rate of decay is less than 10% of the rate of decay initially? (d) Why do these two questions have the same answer?

3. A certain radioactive green substance has a half life of 25 years. We know that the quantity of something with radioactive decay has a formula given by P(t) = Poet, where Po is the initial quantity and k is some constant. (a) Determine k for this given substance. (b) How much time elapses before there is less than 10% of the original amount of the substance present? (c) How much time elapses before the rate of decay is less than 10% of the rate of decay initially? (d) Why do these two questions have the same answer?

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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3. A certain radioactive green substance has a half life of 25 years. We know that the quantity of something with radioactive decay has a formula given by P(t) = Poet, where Po is the initial quantity and k is some constant. (a) Determine k for this given substance. (b) How much time elapses before there is less than 10% of the original amount of the substance present? (c) How much time elapses before the rate of decay is less than 10% of the rate of decay initially? (d) Why do these two questions have the same answer? (e) Show that the formula for P(t) satisfies the property that (f) How long before it is safe to return to Hawkins? dP (t) dt =kP(t).
Transcribed Image Text:3. A certain radioactive green substance has a half life of 25 years. We know that the quantity of something with radioactive decay has a formula given by P(t) = Poet, where Po is the initial quantity and k is some constant. (a) Determine k for this given substance. (b) How much time elapses before there is less than 10% of the original amount of the substance present? (c) How much time elapses before the rate of decay is less than 10% of the rate of decay initially? (d) Why do these two questions have the same answer? (e) Show that the formula for P(t) satisfies the property that (f) How long before it is safe to return to Hawkins? dP (t) dt =kP(t).
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