A construction company has an expenditure rate of E'(x) = e⁰.¹²ˣ dollars per day on a particular paving job and an income rate of I'(x) = 121.1 - e⁰.¹²ˣ dollars per day on the same job, where x is the number of days from the start of the job. The company's profit on that job will equal total income less total expenditures. Profit will be maximized if the job ends at the optimum time, which is the point where the two curves meet.
(a) Find the optimum number of days for the job to last.