Initially, 10 grams of a radioactive substance were found in a sample. It was observed In z that 20% of the initial amount of radioactive substance disintegrated after 2 hours (that is, 8 grams remain after 2 hours). Find the half-life of the radioactive substance (that is, the time it takes for one- half of the initial amount to disintegrate) if the rate of disintegration of the radioactive substance is 1 2 0.7 proportional to the amount of the substance present at time t. You must begin your solution process by considering the proportional relationship presented below. Use the natural logarithm table to the right 1.1 to provide an approximate answer. Your work must support your answer. 4 1.4 1.6 dA a A dt 6 1.8 7 1.9 8 2.1 9 2.2 10 2.3
Initially, 10 grams of a radioactive substance were found in a sample. It was observed In z that 20% of the initial amount of radioactive substance disintegrated after 2 hours (that is, 8 grams remain after 2 hours). Find the half-life of the radioactive substance (that is, the time it takes for one- half of the initial amount to disintegrate) if the rate of disintegration of the radioactive substance is 1 2 0.7 proportional to the amount of the substance present at time t. You must begin your solution process by considering the proportional relationship presented below. Use the natural logarithm table to the right 1.1 to provide an approximate answer. Your work must support your answer. 4 1.4 1.6 dA a A dt 6 1.8 7 1.9 8 2.1 9 2.2 10 2.3
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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Transcribed Image Text:Initially, 10 grams of a radioactive substance were found in a sample. It was observed
that 20% of the initial amount of radioactive substance disintegrated after 2 hours (that is, 8 grams
remain after 2 hours). Find the half-life of the radioactive substance (that is, the time it takes for one-
half of the initial amount to disintegrate) if the rate of disintegration of the radioactive substance is
In z
1
2
0.7
proportional to the amount of the substance present at time t. You must begin your solution process by
3
considering the proportional relationship presented below. Use the natural logarithm table to the right
1.1
to provide an approximate answer. Your work must support your answer.
4
1.4
1.6
dA
a A
6
1.8
dt
1.9
2.1
9
2.2
10
2.3
7,
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