If 200 increases by 2% each day, in how many days will it reach 2000?

11 Answers

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  • Guy
    Lv 7
    1 decade ago
    Best Answer

    Let n = # of days:

    200(1.02)^n = 2000

    1.02^n = 2000/200

    1.02^n = 10

    log(1.02^n) = log(10)

    n*log(1.02) = 1

    n = 1 / log(1.02)

    n = 116.27

    It will take 117 days.

    Note: The people who say the answer is 450 days are wrong because they are not taking into account the fact that it's not 2% of 200 each day, rather it's 2% of 200 the first day, 2% of 204 the second, etc... This is basically a compound interest problem where the interest is compounded daily.

  • 1 decade ago

    if 200 increases by 2%, it will increase by .02(200) or 4 per day. At this rate, it will take 450 days for 200 to increse to 2000.

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  • 1 decade ago

    if n is the number of days

    then 2000= 200(1+0.02)^n

    10=(1.02)^n

    log10=n(log 1.02)

    n = 1/log(1.02)=116.27

    after 117 days the money will be more than 2000

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  • 1 decade ago

    use formula

    2000 = 200 (1+2/100)^n where n= no. of days

    or 10=(1+0.02)^n

    or 1.02^n=10

    or nlog(base 10) 1.02=log10=1

    or n= 1/log1.02

    find log 1.02 and proceed

    you will get n= 117 approx

  • 1 decade ago

    450

  • Anonymous
    1 decade ago

    in 10 dayz

  • 1 decade ago

    200*(1.02)^x = 2000

    (1.02)^x = 10

    x=ln(10) / ln(1.02)

    Press calculator for answer.

  • Nomadd
    Lv 7
    1 decade ago

    116 days and change.

  • len b
    Lv 5
    1 decade ago

    But is it compounded?

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