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- Applications of Exponential and Logarithmic Functions

Still Confused?

Try reviewing these fundamentals first.

Still Confused?

Try reviewing these fundamentals first.

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Start now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

Get Started NowStart now and get better math marks!

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