Results 1 to 2 of 2

Math Help - please help

  1. #1
    Newbie
    Joined
    Aug 2007
    Posts
    5

    Exclamation please help

    The daily output of a product on the
    Tth day of a production run is given by
    q=500(2-e^-0.3t), 0 ≤ t 10.

    (a) Find, to the nearest complete unit, the output on the first day and the tenth day of
    production.
    (b) After how many days will a production level of 900 units be exceeded?
    (c) Sketch the graph of the function.

    Follow Math Help Forum on Facebook and Google+

  2. #2
    Forum Admin topsquark's Avatar
    Joined
    Jan 2006
    From
    Wellsville, NY
    Posts
    9,962
    Thanks
    349
    Awards
    1
    Quote Originally Posted by tondie2 View Post
    The daily output of a product on the
    Tth day of a production run is given by
    q=500(2-e^-0.3t), 0 ≤ t 10.

    (a) Find, to the nearest complete unit, the output on the first day and the tenth day of
    production.
    (b) After how many days will a production level of 900 units be exceeded?
    (c) Sketch the graph of the function.
    I presume the problem is with b) since for a) all you need to do is plug in t = 1 and t = 10.

    So
    q = 500(2 - e^{-0.3t})

    When and for how long is q > 900.

    Let's find out when q = 900.

    900 = 500(2 - e^{-0.3t})

    \frac{9}{5} = 2 - e^{-0.3t}

    e^{-0.3t} = 2 - \frac{9}{5} = \frac{1}{5}

    -0.3t = ln \left ( \frac{1}{5} \right ) = -ln(5)

    t = \frac{ln(5)}{0.3} \approx 5.36479

    So we know that after day 5 q is greater than 900. If you look at the graph in part c) (which I have attached below), you will see that q never goes back down. So q > 900 for days 6, 7, 8, 9, and 10. Thus the answer is 5 days.

    -Dan
    Attached Thumbnails Attached Thumbnails please help-product.jpg  
    Follow Math Help Forum on Facebook and Google+


/mathhelpforum @mathhelpforum