Respuesta :
[tex]\bf \qquad \textit{Amount for Exponential Decay}\\\\
A=P(1 - r)^t\qquad
\begin{cases}
A=\textit{accumulated amount}\\
P=\textit{initial amount}\\
r=rate\to r\%\to \frac{r}{100}\\
t=\textit{elapsed time}\\
\end{cases}\\\\
-------------------------------\\\\
n(x)=7(0.067)^x\implies n(x)=7(1-\stackrel{r}{0.933})^x
\\\\\\
r=0.933\qquad r\%=0.933\cdot 100\implies r=\stackrel{\%}{93.3}[/tex]
Answer: The rate of decay is 93.3%.
Step-by-step explanation:
Since we have given that
The exponential function is given by
[tex]n(x)=7(0.067)^x[/tex]
As we know the general equation of exponential function that is given by
[tex]n(x)=a(1-b)^x[/tex]
Here, a denotes the initial value
1-b denotes the rate of decay.
So, On comparing both the equations, we get that
[tex]1-b=0.067\\\\b=1-0.067\\\\b=0.933=0.933\times 100=93.3\%[/tex]
Hence, the rate of decay is 93.3%.
