The capitalized cost C of an asset is given by C = C₀ +

where C₀ is the original investment, t is the time in years, r is the annual interest rate compounded continuously, and c(t) is the annual cost of maintenance.

Assume the original investment is $650,000, r is 6%, and the maintenance cost is $25000(1+.08t).

Find the capitalized cost of the asset for

a. t = 5 years,

b. t = 10 years,

c. t = forever

c(t)e ttdt