Question

A radioactive substance decreases 5.2% per hour. Initial value of the substance is 120 mg. Write an exponential function that is the amount of substance is the function of time

Answer 1

`\qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{current amount}\\ P=\textit{initial amount}\dotfill &120\\ r=rate\to 5.2\%\to (5.2)/(100)\dotfill &0.052\\ t=hours\\ \end{cases} \\\\\\ A = 120(1 - 0.052)^(t) \implies {\Large \begin{array}{llll} A = 120( 0.948 )^(t) \end{array}}`