The impact of a 5% inflation rate on an $80,000-per-year pension can be severe. If P represents the purchasing power (in dollars) of an $80,000 pension, then the effect of a 5% inflation rate can be modeled by the differential equation dP/dt = - 0.05P, P(0) = 80,000 where t is in years.
(a) Find the particular solution to this differential equation.
(b) Find the purchasing power after 15 years.