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valkas [14]
3 years ago
11

An element with mass 730 grams decays by 27.6% per minute. How much of the element is remaining after 12 minutes, to the nearest

10th of a gram?
Mathematics
2 answers:
Korolek [52]3 years ago
8 0
\bf \qquad \textit{Amount for Exponential Decay}\\\\
A=I(1 - r)^t\qquad 
\begin{cases}
A=\textit{accumulated amount}\\
I=\textit{initial amount}\to &730\\
r=rate\to 27.6\%\to \frac{27.6}{100}\to &0.276\\
t=\textit{elapsed time}\to &12\\
\end{cases}
\\\\\\
A=730(1-0.276)^{12}\implies A=730(0.724)^{12}
8090 [49]3 years ago
7 0

Answer: 15.1 gram

Step-by-step explanation:

The exponential decay equation with rate of decay r in time period t is given by :-

f(x)=A(1-r)^t, A is the initial value .

Given: The initial mass of element=  730 grams

Rate of decay= 27.6%=0.276

Thus, the function represents the amount of element after t minutes is given by ;-

f(x)=730(1-0.276)^x\\\\\Rightarrow\ f(x)=730(0.724)^x

Now, the function represents the amount of element after 12 minutes is given by ;-

f(x)=730(0.724)^{12}\\\\\Rightarrow\ f(x)=15.1420841187\approx15.1\text{ grams}

Hence, 15.1 grams of element remains after 12 minutes.

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