Results 1 to 2 of 2

Math Help - word problem

  1. #1
    Junior Member
    Joined
    Oct 2006
    Posts
    71

    word problem

    A pair of shoes now costs $85 and the price is expected to increase 3% each year.Approximately how many years from now will the price be $100?
    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    10,063
    Thanks
    370
    Awards
    1
    Quote Originally Posted by gracy View Post
    A pair of shoes now costs $85 and the price is expected to increase 3% each year.Approximately how many years from now will the price be $100?
    Note: A 3% increase in the price means you mulitply by 103%, or by 1.03.

    This is essentially a geometric series. Let t be the number of years and P the price of the shoes in dollars. Then:
    P(t) = 85 \cdot (1.03)^t

    So, we want to know t when P = $100.

    100 = 85 \cdot (1.03)^t

    \frac{100}{85} = (1.03)^t

    (1.03)^t = 1.176470588

    Now take the logarithm of both sides. I personally prefer log base e = "ln", but pick which ever base you prefer. The choice does not matter.

    ln \left ( (1.03)^t \right ) = ln(1.176470588)

    t \cdot ln(1.03) = ln(1.176470588)

    t = \frac{ln(1.176470588)}{ln(1.03)} = 5.498156798

    So t = 5.5 years or so.

    -Dan
    Follow Math Help Forum on Facebook and Google+

Similar Math Help Forum Discussions

  1. word problem - the snow plough problem?
    Posted in the Differential Equations Forum
    Replies: 1
    Last Post: October 13th 2011, 01:02 PM
  2. Replies: 3
    Last Post: January 2nd 2011, 08:20 PM
  3. 1 Word problem and 1 function problem
    Posted in the Algebra Forum
    Replies: 8
    Last Post: April 21st 2010, 08:01 AM
  4. Replies: 2
    Last Post: January 10th 2009, 05:49 AM

Search Tags


/mathhelpforum @mathhelpforum