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  1. #1
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    Help

    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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  2. #2
    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

    $\displaystyle P(t) = P_0 e^{rt}$

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

    you are told $\displaystyle P_0 = 1000$

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

    you can then answer the other questions.

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

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

    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

    $\displaystyle P(t) = P_0 e^{rt}$

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

    you are told $\displaystyle P_0 = 1000$

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

    you can then answer the other questions.

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

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

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