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Math Help - Logarithmic function help

  1. #1
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    Post Logarithmic function help

    1. How long would it take for $25 to increase to $500 at 7.6% compounded annually? Round off your answer to the nearest year.

    2. The population of a colony of bacteria doubles every 3 hours. How long, in hours, does it take for the population to be 3.5 times its original size? Answer correct to one decimal place.

    3. Suppose the exponential model of a population growth is given by
    P(t) = P010kt,
    where P0 equals the original or initial population and t is time in hours. Find k, if a population of a culture is 540 now and is 2200 in 11 hours. (Accurate to 3 decimal places)

    4. 210 grams of a radioactive substance decays to 80 grams after 880 years. To the nearest year, what is the half-life of the substance?

    5. Earthquake intensity is given by I = Io(10)m, where Io is the reference intensity and m is magnitude. A particular major earthquake of magnitude 7.4 is 70 times as intense as a particular minor earthquake. The magnitude, to the nearest tenth, of the minor earthquake is

    Logarithmic Applications Formula.

    A = AO (B)^ T/P
    A= Future Amount
    Ao = Intial Amount
    B = Type of growth
    P = Period for Growth to occcur
    T = Elaspsed Time.
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  2. #2
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    Quote Originally Posted by danield3 View Post
    1. How long would it take for $25 to increase to $500 at 7.6% compounded annually? Round off your answer to the nearest year.

    2. The population of a colony of bacteria doubles every 3 hours. How long, in hours, does it take for the population to be 3.5 times its original size? Answer correct to one decimal place.

    3. Suppose the exponential model of a population growth is given by
    P(t) = P010kt,
    where P0 equals the original or initial population and t is time in hours. Find k, if a population of a culture is 540 now and is 2200 in 11 hours. (Accurate to 3 decimal places)

    4. 210 grams of a radioactive substance decays to 80 grams after 880 years. To the nearest year, what is the half-life of the substance?

    5. Earthquake intensity is given by I = Io(10)m, where Io is the reference intensity and m is magnitude. A particular major earthquake of magnitude 7.4 is 70 times as intense as a particular minor earthquake. The magnitude, to the nearest tenth, of the minor earthquake is

    Logarithmic Applications Formula.

    A = AO (B)^ T/P
    A= Future Amount
    Ao = Intial Amount
    B = Type of growth
    P = Period for Growth to occcur
    T = Elaspsed Time.
    Welcome on board!

    You have (obviously) just started with exponential and logarithmic functions - right?

    All your questions are standard exercises. So if you need some help you should show us what you have done so far and where you have difficulties to proceed.
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  3. #3
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    Quote Originally Posted by earboth View Post
    Welcome on board!

    You have (obviously) just started with exponential and logarithmic functions - right?

    All your questions are standard exercises. So if you need some help you should show us what you have done so far and where you have difficulties to proceed.
    I have done some what on 1-4. And I do not know how to do it.

    These are the answers for 1 -4
    1. t=9.120357639
    2.t=5.422064766
    3. k=3.7%
    4.r=0.10965%
    5.?
    I do not know if it is correct. So please tell me these right and help me in 5.
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  4. #4
    A riddle wrapped in an enigma
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    Quote Originally Posted by danield3 View Post
    1. How long would it take for $25 to increase to $500 at 7.6% compounded annually? Round off your answer to the nearest year.
    Hi danield3,

    You might consider posting these one at a time and show as much detail as you can.

    Your first one uses the compound interest formula:

    A=P\left(1+\frac{r}{n}\right)^{nt}

    A = amount of money accumulated after t years, including interest.

    r = annual rate of interest (as a decimal)

    t = number of years the amount is deposited or borrowed for.

    n = number of times the interest is compounded per year

    500=25\left(1+\frac{.076}{1}\right)^{1t}

    20=1.076^t

    \ln 20=t \ln 1.076

    t=\frac{\ln 20}{\ln 1.076} \approx 41 years.
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