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CH10A&10B Alg 2 H
Exponential Functions
| Question | Answer |
|---|---|
| b^1/n=? | n√b |
| b^(m/n)=? | n√b or (n√b)^m |
| Exponential Equation | Variable appears in an exponent (no roots) |
| one-to-one function | for every p and q in the domain of a function, f(p)=f(q) if and only if p=q. |
| Composite function | The function whose value at x is f(g(x)). f and g are combined to produce the comspite: f(g(x))=(fog)(x) |
| Identify function | Maps x to itself, f(x)=x or h(x)=x. |
| *Inverse function | 2 functions are inverse if and only if f(g(x))=x and g(f(x))=x. |
| **a function has an inverse function if and only if...(2) | it passes the horizontal line test; graphs are reflective over y=x |
| how to find the inverse fn | switch x and y, and solve for y |
| general equation of an exponential function | y-k=a(b)^(x-h) |
| what is the origin and horizontal asymptote? | (h,k) and y=k |
| what base value indicates exponential decay or exponential growth? | decay: 0<b<1 and growth: b>1 |
| domain and range of an exponential function? | D=all real #s R={y:y>k} (growth), and {y:y<k} (decay) |
| log function is... | the inverse of an exponential function |
| **product property | logb(MN)=logbM+logbN |
| **quotient property | logb(M/N)=logbM-logbN |
| **power property | logbM^k=k*logbM |
| **compound interest formula | A=P(1+r/n)^nt A=amt accumulated, P=deposit (principal), r=interest rate (%), n=# of times compounded per year, t=time in years |
| **doubling-time growth formula | N=N.(2)^(t/d) N=population currently, N.=initial value (when t=0) |
| **half-life decay formula | N=N.(1/2)^(t/h) h=half life |
| **exponential growth | y=a(1+r)^t (b>1) |
| **exponential decay | y=a(1-r)^t (0<b<1) |
| *common log | log10X |
| *natural log | logeX |
| **properties of the natural log | e^lnx=x, lne^x=x (inverses) |
| **e=? | 2.718 |
| **change of base formula | logaX=logX/loga (base goes to the bottom!) |
Created by:
allyson.lee
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