EXPONENTIAL FUNCTIONS
| General Model for Exponential Functions | y = c(a)kx-p + b | c: Initial value a: Growth or decay factor (growth factor, if a >1; decay factor, if 0 < a <1) k: constant c: initial value b: Constant p: Constant x: independent variable y: dependent variable |
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APPLICATIONS OF EXPONENTIAL FUNCTIONS |
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| Exponential growth (doubling period) |
A = A0 (2)t/D |
A0 : initial amount (t = 0) A: Amount after t years t: time 2: Growth factor D: Doubling period (s, min, hour, day, years, etc.) |
| Exponential decay (half life) |
A = A0 (1/2)t/D |
A0 : initial amount (t = 0) A: Amount after t years t: Number of years 1/2: Decay factor D: Half life (s, min, hour, day, years, etc.) |
| Population estimate |
P = P0bt |
P0: Initial population for t = 0 P: Population after t years b: base (population growth if b >1; population decrease if 0 < b < 1) t: time (years) |
| Exponential function with base e |
A = P ert |
P: Initial amount for t = 0 A: Amount at time t e: base (e = 2.71828182...) r: constant (growth for r > 0; decay for r < 0) t: time |
| Compound Interest |
A = P (1+i)n |
A: Future amount P: Present amount i: Interest rate per compounding period n: Number of compounding period |
| Geometric sequence |
tn = a(r)n-1 |
tn: nth term in the sequence a: First term r: Common ratio n: Number of terms |