Exponential decay: Half-life

Exponential decay: Half-life

In the field of nuclear physics, half-life refers to the amount of time required for radioactive substances to decay into half. In this lesson, we will work on word questions about exponential decay of radioactive substances.
Basic Concepts: Solving exponential equations with logarithms, Solving logarithmic equations
Related Concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions

Lessons

exponential growth/decay: Af=Ai(f)timeperiod { A_f = A_i (f)^{time\over period}}

Af {A_f} : final amount
Ai {A_i} : initial amount
f {f }
: growth/decay factor
half-time→f=12 \to f = {1\over 2}
triple
→f=3\to f = {3}
ten-fold
→f=10 \to f = {10}
increase by 10%→f=(1+10100)=1.1 \to f = {({1 + {10\over 100}}) } { = 1.1}
decrease by 8%→f=(1−8100)=0.92 \to f = {({1 - {8\over 100}}) } { = 0.92}
time {time} : total time given
period {period} : every length of time
  • 1.
    half-life decay

    Strontium-90 is a radioactive substance with a half-life of 28 days.
    How many days will it take for a 200 gram sample of strontium-90 to be
    reduced to 8 grams?

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29.
Logarithms and Exponential Functions
29.1
What is a logarithm?
29.2
Evaluating logarithms without a calculator
29.3
Product rule of logarithms
29.4
Quotient rule of logarithms
29.5
Combining product rule and quotient rule in logarithms
29.6
Solving logarithmic equations
29.7
Evaluating logarithms using change-of-base formula
29.8
Exponential growth and decay by a factor
29.9
Exponential decay: Half-life
29.10
Natural log: ln
CLEP College Math
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