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25 October, 16:28

How many hours will it take a culture of bacteria to increase from 20 to 2000 if the growth rate per hour is 85%

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  1. 25 October, 16:50
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    So you are seeing how much time it'll take so you solve for "t", the time.

    So you take the formula A=Pe^ (rt)

    A=2000 because it's the end value

    P=20 because it's the starting value

    r=.85 since 85%=.85 and. 85 is the rate

    Plug the values in and you get 2000=20e^ (.85t)

    What you do is you divide by 20 so you get 100=e^ (.85t)

    Take the natural logarithm of both sides 'cause of e and a natural log is written as ln so you get

    ln 100=.85t ln e and because you can use the power rule you end up with. 85t ln e and

    ln e=1 so you have ln 100 =.85t so you divide by. 85 so (ln 100) /.85=t and t=5.4178472776331

    hours

    3. Exponential decay:

    A = Pe^ (rt)

    where

    A is the final amount

    P is the initial value

    r is rate of decay

    t is time (years)

    Let's say x is the initial amount then (1/2) x=xe^ (32r)

    I used x because the value isn't given but anyway division by x would give you 1/2=e^ (32r)

    Take the ln of both sides so ln 1/2=32r ln e and then ln e=1 so ln 1/2=32r.

    Divide both sides by 32 and you'd get (ln 1/2) / 32=r and r = - 0.021660849392498

    4. Another depreciation question.

    Each year the item retains 88% of its last-year value.

    Solve: 250,000 (0.88) ^x = 100,000

    0.88^x = 0.4

    x = [log0.4]/[log0.88]

    x = 7.168 years
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