Question

The mass of a radioactive substance follows a continuous exponential decay model, with a decay rate parameter of 1% per day. A sample of this radioactive substance has an initial mass of 2.5kg. Find the mass of the sample after five days.

Answer 1

Answer:

2,38kg

Explanation:

Mass in function of time can be found by the formula: $m_{(t)} =m_{0} e^{-kt}$, where $m_{0}$ is the initial mass, t is the time and k is a constant.

Given that a sample decay 1% per day, that means that after first day you have 99% of mass.

$m_{(1)} =m_{0} e^{-k(1)}$, but $m_{(1)}=\frac{99m_{0} }{100}$, so we have $\frac{99m_{0} }{100}=m_{0}e^{-k}$, then $k=-ln(\frac{99}{100})=0.01$

Now using k found we must to find $m_{(5)}$.

$m_{(5)}=m_{0}e^{-(0.01)5}=2.5kge^{-0.05} =2.5x0.951=2.38kg$