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  • Business Calculus problem, work included. Why am I coming up with the wrong answer?

    The problem is as follows:

    "Plutonium-239 has a decay rate of approximately 0.003% per year. Suppose that plutonium-239 is released into the atmosphere each year for 20 years at a constant rate of 1 lb per year. How much plutonium-239 will remain in the atmosphere after 20 years?"

    My answer:

    The amount of plutonium remaining is given exactly by the definite integral shown, where the chemical is released into the atmosphere at a rate of R(t) pounds per year for T years at a decay rate of k.

    ∫_(t to 0)(R(t) e^kt (dt)

    Substitute the given values in the definition for the future amount. The value of k will be negative because it is decaying.

    ∫(20 to 0) 1 e^(-0.003t)(dt)

    Now, we integrate with respect to t.

    [-333.33e^(-0.003(t)) ](20 to 0)

    Lastly, we evaluate the result over the integral from t = 0 from t = 20.

    -333.33(e^(-0.003(20))-e^(-0.003(0))) ≈ 19.41162802

    Therefore, the approximate amount of plutonium-239 in the atmosphere after 20 years is 19.412 lbs.

    I'm coming up with the answer of 19.412 lbs, but the book says the answer is 19.994 lbs.

    2 AnswersMathematics1 decade ago
  • How do I maximize revenue in this word problem?

    When a theatre owner charges for $5 for admission, there is an average attendance of 180 people. For every $0.10 increase in admission, there is a loss of 1 customer from the average number. What admission should be charged in order to maximize revenue?

    2 AnswersMathematics1 decade ago
  • Why exactly was it so warm in Chicago?

    I am curious about why we had record-breaking temperatures on Tuesday, 2/10/2009. Does anyone have any technical or scientific insight, or a web page that would help explain it?

    2 AnswersWeather1 decade ago
  • Opening band(s) for STP, specifically Chicago.?

    I have tickets to see Stone Temple Pilots next Thursday at Northerly Island Pavilion, but I don't know who the opening band is. It's not printed on the ticket nor can I find it on Ticketmaster or any sort of forum. Any info is appreciated!

    2 AnswersRock and Pop1 decade ago