Anonymous
Anonymous asked in Education & ReferenceHomework Help · 2 months ago

Exponential and logarithmic math problem?

A ring increases in value by 12% per year. In how many years, month, and days will it be four times its original amount?

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  • Bryce
    Lv 7
    2 months ago

    4= 1.12^t

    ln4= tln1.12

    t≈ 12.2325107... years or 372.112975... months or 4464.86640... days

  • 2 months ago

    4p=p*(1+12/100)^n

    solve for n

    that's your problem

  • 2 months ago

    What do you mean by " increase in value" ? It can be increase in value of -- 

    (1) its radius  or  (2) its Area, or even (3) its perimeter. 

    We will find that In any case, the result is same.

    I am solving it for Radius,

    Let the initial Value of Radius  =  R,  so that after " t " years it increases to 4 R @ 12%

    Applying Compound increase formula we get --

    4 R  =  R ( 1 + 12/100 )^t

    =>  4  =   (1.12)^t

    Taking log of both the sides we get --

    => log (4)  =  t log (1.12)

    .... . . ...  log (4). . . . .  0.60205999132796

    => t = ---------------  = -----------------------------  =    12.232510748 years

    . . . .  .  log (1.12) . . . .0. 04921802267018

    =>  t  =  12 years-2 months-23.7 days.  ............... Answer

  • 2 months ago

    @Pramod Kumar

    Ring - the kind that goes on a finger

    A piece of jewelry that increases in value.

    -------------------------------

    Now as to the problem at hand:

    4 = (1.12)^t

    Take the log of both sides

    log4 = t * log1.12

    Divide both sides by log1.12

    t = log4/log1.12

    Use calculator

    t = 12.23251074839941 years

    12 years

    .23251074839941years * 365.25 days/year = 84.9245508529 days

    84.9245508529 days * 1mo/30.41667days = 2.7920397221 months

    2 months

    .7920397221 months * 30.41667days/month = 24.091210854 days

    ~ 24 days

    Approximately,

    12 years, 2 months and 24 days <––––––

    (This could vary by a few days depending on how years and months are calculated)

    From today: November 28, 2020

    it would be February 21, 2033

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  • 2 months ago

    You cannot figure that exactly unless you define a specific start date. That is needed to ensure you account for explicit months (since they vary by number of days each). So I suggest you first figure the interest rate per day. Your class textbook should guide you the rest of the way.

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