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A person starts at time t 0 to pay part of their salary continuously into...

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Calculus

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A person starts at time t 0 to pay part of their salary continuously into an investment fund at a rate of P dollars per year The fund earns interest at a rate r per year compounded continuously The amount of money in the fund after t years M t then satisfies the differential equation dM dt P rM with M 0 0 i Solve the differential equation using the integrating factor method ii If the person can pay in 1 250 each year and the interest rate is 5 how long will it take for the amount of money in the fund to reach 10 000

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