Continuous growth and decay
Examples
Lessons
- 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?
- A radioactive substance decays continuously. If the half-life of the substance
is 5 years, determine the rate of decay.
Free to Join!
StudyPug is a learning help platform covering math and science from grade 4 all the way to second year university. Our video tutorials, unlimited practice problems, and step-by-step explanations provide you or your child with all the help you need to master concepts. On top of that, it's fun — with achievements, customizable avatars, and awards to keep you motivated.
Easily See Your Progress
We track the progress you've made on a topic so you know what you've done. From the course view you can easily see what topics have what and the progress you've made on them. Fill the rings to completely master that section or mouse over the icon to see more details.Make Use of Our Learning Aids
Earn Achievements as You Learn
Make the most of your time as you use StudyPug to help you achieve your goals. Earn fun little badges the more you watch, practice, and use our service.Create and Customize Your Avatar
Play with our fun little avatar builder to create and customize your own avatar on StudyPug. Choose your face, eye colour, hair colour and style, and background. Unlock more options the more you use StudyPug.
Topic Notes
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.
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
Basic Concepts
2
videos
remaining today
remaining today
5
practice questions
remaining today
remaining today