Note
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Exponential Models
Compound Interest
A = P (1 + r / n) ^nt
Terms | Definitions |
|---|---|
A | Expected amount after T years |
P | Principle amount (initial) |
R | interest rate (as decimal) |
N | compounding period |
T | time (in years) |
Compounding Periods | n value |
|---|---|
Yearly | n = 1 |
Semi-annually | n = 2 |
Tri-annually | n = 3 |
Quarterly | n = 4 |
Monthly | n = 12 |
Weekly | n = 52 |
Bi-weekly | n = 26 |
Daily | n = 365 |
Hourly | n = 8760 |
Continuously compounding | A = P * e^rt |
Exponential Growth
A = P (1 + r)^t
Exponential Decay
A = P (1 - r)^t
Common Logs
Log (10) x = y
means 10 & y = 10
10^x and Log (x) are inverses, so:
Log (10^x) = x
10^(Log(x)) = x
Properties
Log (a) + Log (b) = Log (ab)
Log (a) - Log (b) = Log (a / b)
Log (a)^t = t * Log (a)
Log (10)^x = x
Natural Logs
Ln (x) = y means e^y = x
Ln (e^x) = x
e (ln(x)) = x
Properties
Ln a + Ln b = Ln (a*b)
Ln a - Ln b.= Ln (a / b)
Ln a&t = t * Ln a
Ln (e^x) = x
e ^ (Ln x) = x
Radioactive Decay
f(x) = P (0.5) ^ (x / h)
Term | Definition |
|---|---|
P | Initial amount of substance |
H | Half-life of substance |
X | Time |
f(x) | Substance left after X amount of time |
NoteStudied by 2 peopleNoteStudied by 7 peopleNoteStudied by 10 peopleNoteStudied by 2 peopleNoteStudied by 482 peopleNoteStudied by 12 people