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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.

17.

Exponential and Logarithmic Functions

17.1

Solving logarithmic equations

17.2

Graphing exponential functions

17.3

Graphing transformations of exponential functions

17.4

Finding an exponential function given its graph

17.5

Graphing logarithmic functions

17.6

Finding a logarithmic function given its graph

17.7

Finance: compound interest

17.8

Continuous growth and decay

17.9

Natural log: ln

17.10

Solving exponential equations with logarithms

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