The exponential decay law
dy
dt
= −λy, λ > 0
may be used to model decay of a radioactive isotope, or any other quantity that is
decreasing at a rate proportional to its own magnitude. This is just the exponential
growth model with a negative growth rate k = −λ. As is often done, I have put the
sign into the differential equation so that the parameter λ is positive. In this question
take the unit of time to be years. λ is called the decay rate.
(a) By substitution into the differential equation verify that (as expected) y(t) = ce−λt
is a solution of the exponential decay law for any constant c.

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