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Let Q(t)=The amount of a substance at time t. The rate of change in the amount of radioactive material is proportional to the amount present. Q'(t) = kQ(t), . for a constant k Notes: k is referred as the growth rate if k > 0, and k as the decay rate if k < 0. • Half-life: The time required for a quantity to reduce to half of its original amount. Let T denote the half-life period. • Doubling time: The amount of time it takes for a quantity to double in size. Example: Lead has a half-life of 22 years. How long will it take to be reduced to 1/10 its original amount?

Let Q(t)=The amount of a substance at time t. The rate of change in the amount of radioactive material is proportional to the amount present. Q'(t) = kQ(t), . for a constant k Notes: k is referred as the growth rate if k > 0, and k as the decay rate if k < 0. • Half-life: The time required for a quantity to reduce to half of its original amount. Let T denote the half-life period. • Doubling time: The amount of time it takes for a quantity to double in size. Example: Lead has a half-life of 22 years. How long will it take to be reduced to 1/10 its original amount?

Trigonometry (MindTap Course List)
Trigonometry (MindTap Course List)
10th Edition
ISBN:9781337278461
Author:Ron Larson
Publisher:Ron Larson
Chapter6: Topics In Analytic Geometry
Section: Chapter Questions
Problem 33CT
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Let Q(t)=The amount of a substance at time t. The rate of change in the amount of radioactive material is proportional to the amount present. Q'(t) = kQ(t), . for a constant k Notes: k is referred as the growth rate if k > 0, and k as the decay rate if k < 0. • Half-life: The time required for a quantity to reduce to half of its original amount. Let T denote the half-life period. • Doubling time: The amount of time it takes for a quantity to double in size. Example: Lead has a half-life of 22 years. How long will it take to be reduced to 1/10 its original amount?
Transcribed Image Text:Let Q(t)=The amount of a substance at time t. The rate of change in the amount of radioactive material is proportional to the amount present. Q'(t) = kQ(t), . for a constant k Notes: k is referred as the growth rate if k > 0, and k as the decay rate if k < 0. • Half-life: The time required for a quantity to reduce to half of its original amount. Let T denote the half-life period. • Doubling time: The amount of time it takes for a quantity to double in size. Example: Lead has a half-life of 22 years. How long will it take to be reduced to 1/10 its original amount?
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