Question

The mass of a radioactive substance follows a continuous exponential decay model. A sample of this radioactive substance has an initial mass of 757 kg and decreases continuously at a relative rate of 7% per day. Find the mass of the sample after three days.Do not round any intermediate computations, and round your answer to the nearest tenth.

Answer 1

The exponential decay model is given by:

$y(t)=a\cdot e^{-kt}$

Where:

a = Initial amount

k = Percent decrease

t = time

Therefore:

$\begin{gathered} a=757 \\ k=0.07 \\ t=3 \\ y(3)=757\cdot e^{-0.07\cdot3} \\ y(3)=613.6\operatorname{kg} \end{gathered}$