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\(\)

\(\bullet\text{ Exponential Functions}\)
\(\,\,\,\,\,\,\,\,y=a(b)^x\)

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

\(\bullet\text{ Half Life Questions}\)
\(\,\,\,\,\,\,\,\,A_t=A_0e^{kt}\)

\(\bullet\text{ Graphing Exponential Functions}\)
\(\,\,\,\,\,\,\,\,f(x)=2^{x-1}-2\,\, \)

\(\bullet\text{ Inverse of Exponential Functions}\)
\(\,\,\,\,\,\,\,\,f^{-1}(x)=\log_5(x-1)\)