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Notes

\(e \approx 2.71828 \)

\(e= \displaystyle \lim_{n\to \infty} \left(1+\frac{1}{n}\right)^n \)

\(e= \displaystyle\sum_{n=0}^{\infty}\frac{1}{n!}\)

\(e= \displaystyle \lim_{x\to 0^+} x^{\frac{1}{\ln{x}}} \)

\(\ln(x) = \log_e (x) \)

See Related Pages\(\)

\(\bullet\text{ Half Life Exponential Decay}\)
\(\,\,\,\,\,\,\,\,A_t=A_0e^{kt}…\)

\(\bullet\text{ Compound Interest}\)
\(\,\,\,\,\,\,\,\,A=P\left(1+\frac{r}{n} \right)^{nt}…\)

\(\bullet\text{ Graphing Exponential Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=2^{x}…\)

\(\bullet\text{ Inverse of Exponential Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=2^x \rightarrow f^{-1}(x)=log_{2}(x)…\)

\(\bullet\text{ Logistic Function}\)
\(\,\,\,\,\,\,\,\,f(x)= \displaystyle \frac{L}{1+e^{-k(x-x_0)}}…\)

\(\bullet\text{ Domain and Range Logarithmic Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=log(x) \rightarrow \text{Domain:} x\gt0… \)

\(\bullet\text{ Graphing Logarithmic Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=log_{2}(x)\)

\(\bullet\text{ Solving Logarithmic Equations}\)
\(\,\,\,\,\,\,\,\,\log_{2}(5x)=\log_{2}(2x+12)…\)

\(\bullet\text{ Inverse of Logarithmic Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=log_{2}(x) \rightarrow f^{-1}(x)=2^x\)

\(\bullet\text{ Derivatives- ln(x)}\)
\(\,\,\,\,\,\,\,\,\displaystyle\frac{d}{dx}[ln(x)]= \displaystyle \frac{1}{x}\)

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