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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: 14:12
- Lesson: 27:21

We now have a better understanding of how the compounding frequency will affect the amount we wish to grow or decay. But what if we are dealing with something, say, that compounds every minute, second, or even millisecond? This concept is also known as continuous compounding. In this section, we will see a slight variation of an exponential growth and decay formula that models continuous exponential growth/decay.

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

Continuous Growth/Decay: ${ A_f = A_i e^{rt}}$

${A_f}$: final amount

${A_i}$ : initial amount

${e }$ : constant = 2.718…

${r }$ : rate of growth/decay

• growth rate of 7% $\to {r = {7\over100} = 0.07}$

• growth rate of 15%$\to {r = - {15\over100} = - 0.15}$

${t }$ : total time given

${A_f}$: final amount

${A_i}$ : initial amount

${e }$ : constant = 2.718…

${r }$ : rate of growth/decay

• growth rate of 7% $\to {r = {7\over100} = 0.07}$

• growth rate of 15%$\to {r = - {15\over100} = - 0.15}$

${t }$ : total time given

- 1.On Aiden's 10-year-old birthday, he deposited $20 in a savings account that

offered an interest rate of 4% compounded continuously. How much money

will Aiden have in the account when he retires at the age of 60? - 2.A radioactive substance decays continuously. If the half-life of the substance

is 5 years, determine the rate of decay.

13.

Applications of Exponential and Logarithmic Functions

13.1

Exponential growth and decay by a factor

13.2

Exponential decay: Half-life

13.3

Exponential growth and decay by percentage

13.4

Finance: Compound interest

13.5

Continuous growth and decay

13.6

Logarithmic scale: Richter scale (earthquake)

13.7

Logarithmic scale: pH scale

13.8

Logarithmic scale: dB scale

13.9

Finance: Future value and present value

We have over 1040 practice questions in AU Year 12 Maths for you to master.

Get Started Now13.1

Exponential growth and decay by a factor

13.2

Exponential decay: Half-life

13.3

Exponential growth and decay by percentage

13.4

Finance: Compound interest

13.5

Continuous growth and decay

13.6

Logarithmic scale: Richter scale (earthquake)

13.7

Logarithmic scale: pH scale

13.8

Logarithmic scale: dB scale

13.9

Finance: Future value and present value