Consider the following situations that generate a sequence.

a. Write out the first five terms of the sequence.

b. Find an explicit formula for the terms of the sequence.

c. Find a recurrence relation that generates the sequence.

d. Using a calculator or a graphing utility, estimate the limit of the sequence or state that it does not exist.

A material transmutes 50% of its mass to another element every 10 years due to radioactive decay. Let M_n be the mass of the radioactive material at the end of the nth decade, where the initial mass of the material is M₀ = 20 g.