An investment of $500,000 is made in a new chemical process for which revenues occur as discrete cash flows and costs occur as continuous cash flows. The functional form for revenues is given by f(t) = $800,000(0.8)t , t = 1, 2, ..., 20, with t measured in years. The functional form for costs is given by f(t) = $40,000t, 0 < t < 10 and f(t) = $40,000(20 t), 10 < t < 20, with t measured in years. Compute the present worth of the investment using a 10% per annum continuous compound interest rate.