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- Applications of Exponential and Logarithmic Functions

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Try reviewing these fundamentals first.

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Try reviewing these fundamentals first.

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Get Started Now- Lesson: 110:11

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.

Related concepts: Derivative of inverse trigonometric functions, Derivative of logarithmic functions,

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

${A_f}$: final amount

${A_i}$: initial amount

${f }$ : growth/decay factor

half-time$\to f = {1\over 2}$

triple$\to f = {3}$

ten-fold$\to f = {10}$

increase by 10%$\to f = {({1 + {10\over 100}}) } { = 1.1}$

decrease by 8%$\to f = {({1 - {8\over 100}}) } { = 0.92}$

${time}$ : total time given

${period}$ : every length of time

${A_f}$: final amount

${A_i}$: initial amount

${f }$ : growth/decay factor

half-time$\to f = {1\over 2}$

triple$\to f = {3}$

ten-fold$\to f = {10}$

increase by 10%$\to f = {({1 + {10\over 100}}) } { = 1.1}$

decrease by 8%$\to f = {({1 - {8\over 100}}) } { = 0.92}$

${time}$ : total time given

${period}$ : 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?

19.

Applications of Exponential and Logarithmic Functions

19.1

Exponential growth and decay by a factor

19.2

Exponential decay: Half-life

19.3

Exponential growth and decay by percentage

19.4

Finance: Compound interest

19.5

Continuous growth and decay

19.6

Logarithmic scale: Richter scale (earthquake)

19.7

Logarithmic scale: pH scale

19.8

Logarithmic scale: dB scale

19.9

Finance: Future value and present value

We have over 1620 practice questions in UK Year 12 Maths for you to master.

Get Started Now19.1

Exponential growth and decay by a factor

19.2

Exponential decay: Half-life

19.3

Exponential growth and decay by percentage

19.4

Finance: Compound interest

19.5

Continuous growth and decay

19.6

Logarithmic scale: Richter scale (earthquake)

19.7

Logarithmic scale: pH scale

19.8

Logarithmic scale: dB scale

19.9

Finance: Future value and present value