Question

What is the rate of decay, as a percent, for the following function n(x)=7(0.067)^x

Answer 1

`\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 (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}`

Answer 2

Answer: The rate of decay is 93.3%.

Explanation:

Since we have given that

The exponential function is given by

`n(x)=7(0.067)^x`

As we know the general equation of exponential function that is given by

`n(x)=a(1-b)^x`

Here, a denotes the initial value

1-b denotes the rate of decay.

So, On comparing both the equations, we get that

`1-b=0.067\\\\b=1-0.067\\\\b=0.933=0.933* 100=93.3\%`

Hence, the rate of decay is 93.3%.