What is the difference between compound interest and exponential growth?
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Compound growth is growth in intervals. One example is you Han have money compounded monthly, weekly, daily , etc. That means that ever day/week/month the amount of money you have increases by a factor. For example, if you have $100 in a bank and they compound your money monthly at 5%, then after 1 month you would have $105, then $111 or something like that, every month multiplying by 1.05.
Continuous growth is growth continuously. It would be every instant multiplying by a constant. For example, if you compound money you multiply the money essentially by (1+1/n)^nt where n is the number of times it is compounded and 1/n would be the percentage (the actual formula is slightly different and will be left as an exersize). Taking the limit as n approaches infinity, you get e^t where e=2.71828182845..... So the exponential growth formula is Pe^rt where P is the initial amount and r is a rate.
Continuous growth is growth continuously. It would be every instant multiplying by a constant. For example, if you compound money you multiply the money essentially by (1+1/n)^nt where n is the number of times it is compounded and 1/n would be the percentage (the actual formula is slightly different and will be left as an exersize). Taking the limit as n approaches infinity, you get e^t where e=2.71828182845..... So the exponential growth formula is Pe^rt where P is the initial amount and r is a rate.
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Answer:
The opposite of growth is decay the opposite of exponential is logarithmic.
Exponential growth :
Exponential growth is a pattern of data that shows greater increases with passing time, creating the curve of an exponential function.
Logarithmic growth :
In microbiology, the rapidly growing exponential growth phase of a cell culture is sometimes called logarithmic growth.
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