Question

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

Answer 1

Answer: The rate of decay is 93.3%.

Step-by-step 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

$1-b=0.067\\\\b=1-0.067\\\\b=0.933=0.933\times 100=93.3\%$

Hence, the rate of decay is 93.3%.

Answer 2

$\bf \qquad \textit{Amount for Exponential Decay}\\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\\ r=rate\to r\%\to \frac{r}{100}\\ t=\textit{elapsed time}\\ \end{cases}\\\\ -------------------------------\\\\ n(x)=7(0.067)^x\implies n(x)=7(1-\stackrel{r}{0.933})^x \\\\\\ r=0.933\qquad r\%=0.933\cdot 100\implies r=\stackrel{\%}{93.3}$