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Math Help - Compound and Continuously Compounded Interest questions

  1. #1
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    Compound and Continuously Compounded Interest questions

    1.) How long will it take $2500 to reach a value of $8000 if it is earning 6.5% annual interest compounded continuously?

    Since it is compounded continuously, I have to use the Pe^rt formula. It is asking me how long it takes for the task to be completed. How do I find the time?

    2.) An equation that can be used to predict the population of a bird that is on the endangered species list is: Predicted population = Current population x 9^-(years/9)

    The equation predicts the number of surviving birds over the next fifteen years if no measures are taken to protect the population.

    It has been determined that if the population drops below 150 birds, it may not be possible to avoid extinction without removing the birds from the wild and raising them in captivity. Will the population fall below 150 in the next 15 years? If yes when?

    On that question part, do I need to plug in 15 years or no?
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  2. #2
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    Re: Compound and Continuously Compounded Interest questions

    problem1 continously compounds

    8000/2500 = e^rt
    ln 3.2 = ln e^rt
    1.163=rt lne
    t=1.163/0.065 lne=1
    t=17.9 years
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  3. #3
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    Re: Compound and Continuously Compounded Interest questions

    Two more questions:

    3.) A colony of bacteria being grown in a jog of apple cider is known to triple every 5 hours. We know that the number of bacteria at 8 a.m. was 6000.
    How many bacteria would be in the colony at 11 am (i.e. three hours after 8 a.m.)?

    How do I create an equation in this context?

    4.) The number of cars in the USA can be modeled by the equation: N=29(1.036)^t where N is the number of millions of passenger cars in the United States and t is the number of years after 1940. In what year was the number of passenger cars triple the number of cars in 1940?

    Do I need to plug in 1940 in the equation or do I need to figure out a number for it?
    Last edited by ele30006; April 30th 2013 at 04:55 PM.
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  4. #4
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    Re: Compound and Continuously Compounded Interest questions

    3 use geometric progression
    first term = 6000 5th term = 18000=ar^n-1 = 6000^4
    r=1.316 growthper hr
    3 hour 6000*(1.316)^2=10391
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