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Mathematics
Mathematics
Problem
A radioactive sample obeys
d
M
d
t
=
−
0.05
M
\frac{dM}{dt}=-0.05M
d
t
d
M
=
−
0.05
M
for
0
≤
t
≤
4
days
0\le t\le 4\,\text{days}
0
≤
t
≤
4
days
. At
t
=
4
days
t=4\,\text{days}
t
=
4
days
, new shielding is added and for
t
>
4
days
t>4\,\text{days}
t
>
4
days
the decay law becomes
d
M
d
t
=
k
M
\frac{dM}{dt}=kM
d
t
d
M
=
k
M
, where
k
k
k
is constant. Given
M
(
0
)
=
50
g
M(0)=50\,\text{g}
M
(
0
)
=
50
g
and
M
(
10
)
=
20
g
M(10)=20\,\text{g}
M
(
10
)
=
20
g
, determine the value of
k
k
k
(include units).
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