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- Applications of Exponential and Logarithmic Functions
Continuous growth and decay
- Lesson: 14:12
- Lesson: 27:21
Continuous growth and decay
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
Lessons
Continuous Growth/Decay: Af=Aiert
Af: final amount
Ai : initial amount
e : constant = 2.718…
r : rate of growth/decay
• growth rate of 7% →r=1007=0.07
• growth rate of 15%→r=−10015=−0.15
t : total time given
Af: final amount
Ai : initial amount
e : constant = 2.718…
r : rate of growth/decay
• growth rate of 7% →r=1007=0.07
• growth rate of 15%→r=−10015=−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.
Do better in math today
43.
Applications of Exponential and Logarithmic Functions
43.1
Exponential growth and decay by a factor
43.2
Exponential decay: Half-life
43.3
Exponential growth and decay by percentage
43.4
Finance: Compound interest
43.5
Continuous growth and decay
43.6
Logarithmic scale: Richter scale (earthquake)
43.7
Logarithmic scale: pH scale
43.8
Logarithmic scale: dB scale
43.9
Finance: Future value and present value
Don't just watch, practice makes perfect
Practice topics for Applications of Exponential and Logarithmic Functions
43.1
Exponential growth and decay by a factor
43.2
Exponential decay: Half-life
43.3
Exponential growth and decay by percentage
43.4
Finance: Compound interest
43.5
Continuous growth and decay
43.6
Logarithmic scale: Richter scale (earthquake)
43.7
Logarithmic scale: pH scale
43.8
Logarithmic scale: dB scale
43.9
Finance: Future value and present value