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math 242

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It is estimated that the demand for a manufacturer's product is increasing exponentially at an instantaneous rate of 7% per year. If the current demand is increasing by 7000 units per year and if the price remains fixed at $100 per unit, how much revenue will the manufacturer receive from the sale of the product over the next 4 years?

  • math 242 - ,

    since "demand is increasing at an instantaneous rate of 7% a year" this means that d'(t)=pe^kt where k=0.07
    now, "current demand is increasing by 7000 units per year" means that the principal demand is 7000, so p=7000.
    then, "price remains fixed at $100 per unit" and since we are looking for revenue and not demand, and revenue=unit*price, so unit=7000 and price=100, so multiply those which gives you 700,000 and insert for p, so p actually =700,000 for revenue, not demand.
    the last part "how much revenue will the manufacturer receive over the next 4 years. so you just use the fundamental theorum of calculus, and insert t=4 minus t=0, and you have your answer in terms of revenue not demand. :)

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