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    The population, P, of bacteria in an experiment can be modelled by the formula P = 100e0.4t,
    where t is the time in hours after the experiment began.

    How many whole hours after the experiment began does the population of bacteria first exceed 1 million, according to the model?
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    ok so you need to set up the equation. you know P = population and you want to know when the population > 1,000,000

    therefore:

    1,000,000 > 100e^0.4t

    rearrange and take logs to find the value of t.
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    Do I need to know what e is?
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    (Original post by hollyeb3)
    Do I need to know what e is?
    e is most likely Euler's number. It's on your calculator
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    (Original post by have)
    e is most likely Euler's number. It's on your calculator
    lool how jarring. OP u dont need to know e because it gets removed after u find ln (ln= loge)
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    (Original post by hollyeb3)
    Do I need to know what e is?
    the "ln" button is the button for logarithm with base e, e being Euler's number which is irrational and transcendental (just like pi), equal to approx 2.71828.

    Here's what you should know about e for A-level:
    \dfrac{d}{dx} e^x = e^x which means it will come up loads in questions relating to rate of change, because for e^x, the rate of change is equal to the value.

    \dfrac{d}{dx} a*e^{kx} = ka*e^{kx}

    \int e^x dx = e^x + c

    and just for fun
    \displaystyle\lim_{n\to \infty} \left(1 + \dfrac{1}{n} \right)^n = e
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    (Original post by hollyeb3)
    The population, P, of bacteria in an experiment can be modelled by the formula P = 100e0.4t,
    where t is the time in hours after the experiment began.

    How many whole hours after the experiment began does the population of bacteria first exceed 1 million, according to the model?
    100e^0.4t > 1000000
    I divide both sides by 100;
    e^0.4t = 10000
    now solve ?
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