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  1. #1
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    The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after three days? How long is it until there are 10000 mosquitoes?
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    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dc52789 View Post
    The population of a colony of mosquitoes obeys the law of uninhibited growth. If there are 1000 mosquitoes initially and there are 1800 after 1 day, what is the size of the colony after three days? How long is it until there are 10000 mosquitoes?
    do you know what formula to use? the exponential growth formula

    P(t) = P_0 e^{rt}

    where P(t) is the population after time t, P_0 is the initial population, and r is the rate of growth.

    you are told P_0 = 1000

    you are also told P(1) = 1800. you can use that to find r. then you can fill in the unknowns in the formula above, except for P(t) and t of course.

    you can then answer the other questions.

    the size of the population after 3 days is given by P(3).

    to find out how long it takes the population to become 10000, set P(t) = 10000 and solve for t

    Quote Originally Posted by dc52789 View Post
    bump
    you are aware that bumping is against the rules, right?
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  3. #3
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    Quote Originally Posted by Jhevon View Post
    do you know what formula to use? the exponential growth formula

    P(t) = P_0 e^{rt}

    where P(t) is the population after time t, P_0 is the initial population, and r is the rate of growth.

    you are told P_0 = 1000

    you are also told P(1) = 1800. you can use that to find r. then you can fill in the unknowns in the formula above, except for P(t) and t of course.

    you can then answer the other questions.

    the size of the population after 3 days is given by P(3).

    to find out how long it takes the population to become 10000, set P(t) = 10000 and solve for t

    you are aware that bumping is against the rules, right?
    I know that now.
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  4. #4
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    This is what I have so far

    I was finding r so this is what I tried to do.

    P(t) = Poe^rt
    1800 = 1000e^(1)r
    1.8 = e^1r
    ln 1.8 = ln e^r
    ln 1.8 = r
    0.588 = r
    Is this right?
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  5. #5
    is up to his old tricks again! Jhevon's Avatar
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    Quote Originally Posted by dc52789 View Post
    I was finding r so this is what I tried to do.

    P(t) = Poe^rt
    1800 = 1000e^(1)r
    1.8 = e^1r
    ln 1.8 = ln e^r
    ln 1.8 = r
    0.588 = r
    Is this right?
    yes. i suppose your professor requires 3 decimal places?

    so now you know P(t) = 1000e^{0.588t}, you can answer the rest of the questions
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  6. #6
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    Quote Originally Posted by Jhevon View Post
    yes. i suppose your professor requires 3 decimal places?

    so now you know P(t) = 1000e^{0.588t}, you can answer the rest of the questions
    Wow...that really helps a lot. Thanks.
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