• A quantity N undergoes exponential decay if it decreases at a rate proportional to its own value. As a function of t, such a quantity must satisfy N(t) = Noe- where No is the initial value of N at time t = 0, and A> 0 is a constant, called the decay constant of N with respect to t. Let N(t) be the mass of a sample of the radioactive isotope carbon-14 after t thousand years. With these assumptions, the mass is known to have decay constant A = 0.12 with respect to t.
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•  (a)  Suppose the sample has an initial mass of 100 kilograms. Write a function that gives the mass of the sample in kilograms after t thousand years.
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• (b) Find the instantaneous rate of change of the sample's mass after 3000 years.