Calculus

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The machine earns the company revenue at a continuous rate of 62000 t + 38000 dollars per year during the first six months of operation, and at the continuous rate of $69000 per year after the first six months. The cost of the machine is $170000. The interest rate is 5% per year, compounded continuously.

a) Find the present value of the revenue earned by the machine during the first year of operation. Round your answer to the nearest cent.

b) Determine how long it will take for the machine to pay for itself; that is, how long until the present value of the revenue is equal to the cost of the machine. Round your answer to the nearest hundredth.

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