A radioactive substance decays in such a way that the amount of mass remaining after t days is given by the function
where m(t) is measured in kilograms.
Find the mass at time t = 0.
How much of the mass remains after 42 days?
+33665 The mass at time 0 is found by replacing t by zero in 10e-0.013t
Since e0 = 1 this means the mass at time zero is just 10 kg.
Replace t by 42 to find the mass after 42 days (assuming that the decay constant has units of days-1)
$${\mathtt{massafter42days}} = {\mathtt{10}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\mathtt{0.013}}{\mathtt{\,\times\,}}{\mathtt{42}}\right)} \Rightarrow {\mathtt{massafter42days}} = {\mathtt{5.792\: \!622\: \!313\: \!807\: \!82}}$$
So approximately 5.79kg remain after 42 days.
+33665 The mass at time 0 is found by replacing t by zero in 10e-0.013t
Since e0 = 1 this means the mass at time zero is just 10 kg.
Replace t by 42 to find the mass after 42 days (assuming that the decay constant has units of days-1)
$${\mathtt{massafter42days}} = {\mathtt{10}}{\mathtt{\,\times\,}}{{\mathtt{e}}}^{{\mathtt{\,-\,}}\left({\mathtt{0.013}}{\mathtt{\,\times\,}}{\mathtt{42}}\right)} \Rightarrow {\mathtt{massafter42days}} = {\mathtt{5.792\: \!622\: \!313\: \!807\: \!82}}$$
So approximately 5.79kg remain after 42 days.
