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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: 19:41

The growth/decay factor "(1+r)" dictates the rate of exponential growth and decay. We will work on questions related to growth/decay factor in this lesson.

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.triple growth

A certain type of bug can triple its population every 10 years.

How many bugs will there be in 50 weeks if there are 76 bugs today?

17.

Applications of Exponential and Logarithmic Functions

17.1

Exponential growth and decay by a factor

17.2

Exponential decay: Half-life

17.3

Exponential growth and decay by percentage

17.4

Finance: Compound interest

17.5

Continuous growth and decay

17.6

Logarithmic scale: Richter scale (earthquake)

17.7

Logarithmic scale: pH scale

17.8

Logarithmic scale: dB scale

17.9

Finance: Future value and present value

We have over 1290 practice questions in A-Level Maths for you to master.

Get Started Now17.1

Exponential growth and decay by a factor

17.2

Exponential decay: Half-life

17.3

Exponential growth and decay by percentage

17.4

Finance: Compound interest

17.5

Continuous growth and decay

17.6

Logarithmic scale: Richter scale (earthquake)

17.7

Logarithmic scale: pH scale

17.8

Logarithmic scale: dB scale

17.9

Finance: Future value and present value