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Notes
| \({\text{Exponential Models}}\) | |
| \(\underline{\text{Exponential Growth}}\) | \(\underline{\text{Exponential Decay}}\) |
|---|---|
| \(y=a(1+r)^t\) | \(y=a(1-r)^t\) |
| \(y={\text{value at time t}}\) \(a={\text{value at time 0}}\) \(r={\text{growth/decay rate}}\) \(t={\text{time}}\) |
|
Practice Problems
Identify whether each exponential model is growth or decay, then give the rate and the initial value.
\(\textbf{1)}\) \(y=4(\frac{3}{4})^t\)
\(\textbf{2)}\) \(y=.5(1.78)^t\)
\(\textbf{3)}\) \(y=3(.78)^t\)
\(\textbf{4)}\) \(y=4(3)^t\)
\(\textbf{5)}\) \(y=2(.1)^t\)
See Related Pages\(\)
\(\bullet\text{ Exponential Functions}\)
\(\,\,\,\,\,\,\,\,y=a(b)^x\)
\(\bullet\text{ Compound Interest}\)
\(\,\,\,\,\,\,\,\,A=P\left(1+\frac{r}{n} \right)^{nt}\,\,\,\,\,\,\,\,A=P e^{rt}\)
\(\bullet\text{ Half Life Questions}\)
\(\,\,\,\,\,\,\,\,A_t=A_0e^{kt}\)
\(\bullet\text{ Graphing Exponential Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=2^{x-1}-2\,\, \)
\(\bullet\text{ Inverse of Exponential Functions}\)
\(\,\,\,\,\,\,\,\,f^{-1}(x)=\log_5(x-1)\)
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