A marine biologist measures the presence of a pollutant in an ocean and concludes that the concentration, C, in parts per million (ppm), as a function of the population, P, of the people who visit the beach is given by C(P) = 1.38P+ 97.4 . The population of people visiting the beach, in thousands, can be modeled by P(t) = 12 (1.078)^t where t is the time in years since the first measurement.

a) Determine an equation, in simplified form, for the concentration of pollutant as a function of the number of years since the first measurement.

b) How long (to the nearest year) will it take for the concentration to reach 180 ppm?