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Sagot :
Using separation of variables, it is found that the expression for the mass, M, at any time t, is given by:
[tex]M(t) = 150e^{-kt}[/tex]
What is separation of variables?
In separation of variables, supposing a differential equation in the format [tex]\frac{dy}{dx}[/tex], we place all the factors of y on one side of the equation with dy, all the factors of x on the other side with dx, and integrate both sides.
In this problem, the differential equation is:
[tex]\frac{dM}{dt} = -kM[/tex]
Then, applying separation of variables:
[tex]\frac{dM}{M} = -k dt[/tex]
[tex]\int \frac{dM}{M} = \int -k dt[/tex]
[tex]\ln{M} = -kt + C[/tex]
[tex]M(t) = M(0)e^{-kt}[/tex]
The initial mass is of M(0) = 150, hence:
[tex]M(t) = 150e^{-kt}[/tex]
More can be learned about separation of variables at https://brainly.com/question/14318343
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