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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: 18:51
- Lesson: 27:32

Exponential growth/decay rates can be presented in percentages. We will work on questions of this kind in this lesson.

Basic Concepts: Solving logarithmic equations

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.exponential growth/decay by percentage

The population of rabbits is increasing by 70% every 6 months.

Presently there are 500 rabits. How many years will it take for

the population to reach 1,000,000? - 2.exponential growth/decay by percentage

The intensity of light is reduced by 2% for each meter that a diver

descends below the surface of the water. At what depth is the intensity of

light only 10% of that at the surface?

8.

Applications of Exponential and Logarithmic Functions

8.1

Exponential growth and decay by a factor

8.2

Exponential decay: Half-life

8.3

Exponential growth and decay by percentage

8.4

Finance: Compound interest

8.5

Continuous growth and decay

8.6

Logarithmic scale: Richter scale (earthquake)

8.7

Logarithmic scale: pH scale

8.8

Logarithmic scale: dB scale

8.9

Finance: Future value and present value

We have over 770 practice questions in NZ Year 13 Maths for you to master.

Get Started Now8.1

Exponential growth and decay by a factor

8.2

Exponential decay: Half-life

8.3

Exponential growth and decay by percentage

8.4

Finance: Compound interest

8.5

Continuous growth and decay

8.6

Logarithmic scale: Richter scale (earthquake)

8.7

Logarithmic scale: pH scale

8.8

Logarithmic scale: dB scale

8.9

Finance: Future value and present value