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Math Help - Growth function

  1. #1
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    Growth function

    The number of minutes it takes for a worker to assemble a particular item depends on his/her experience in performing the job. The average assembly time can be modelled by the following function A(t)= 20 + 3t/t + 1 , where t =number of days on the job, and A(t) is measured in minutes. An expert can assemble an item in 3 minutes. A worker is said to be proficient (very good) if they can assemble an item in 5 minutes.


    Evaluate A(t) for t = 0 and as t -> +infinity. Interpret your answer. State practical domain for this function
    . How many days(weeks) does it take for a worker to get proficient?
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  2. #2
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    Quote Originally Posted by Snowboarder View Post
    The number of minutes it takes for a worker to assemble a particular item depends on his/her experience in performing the job. The average assembly time can be modelled by the following function A(t)= 20 + 3t/t + 1 , where t =number of days on the job, and A(t) is measured in minutes. An expert can assemble an item in 3 minutes. A worker is said to be proficient (very good) if they can assemble an item in 5 minutes.


    Evaluate A(t) for t = 0 and as t -> +infinity. Interpret your answer. State practical domain for this function
    . How many days(weeks) does it take for a worker to get proficient?
    Unfortunately it is not clear what you mean by A(t):

    A(t)=\frac{20+3t}{t+1} ... or ... A(t)=20+\frac{3t}{t+1} ... or ... A(t)=20+\frac{3t}{t}+1 ...

    I take the first version.

    A(0) = \frac{20}1 = 20 \ min ... Obviously this is the time which an absolute beginner will need.

    Since \lim_{t \mapsto \infty} A(t) = 3 the domain of A is (3, 20]

    But: Since you never will reach A(t) = 3 with a final amount of t you'll never become an expert.

    The state of proficiency is reached if A(t) = 5

    \frac{20+3t}{t+1}=5~\iff~20+3t=5t+5~\iff~15=2t ~\iff~t=\frac{15}2 ... That means after 7 weeks a worker has reached the state of a profi.
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  3. #3
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    thanks one more time earboth

    One more question.

    Equation for flight rocket is h(t) = -110t^2 + 2009.3t + 0.9 where h(t) is the height in meters above the ground after t seconds.

    What is the practical domain of the function. Explain your answear.
    Does the model seem realistic. Justify
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  4. #4
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    Quote Originally Posted by Snowboarder at 12:18am today View Post
    thanks one more time earboth

    One more question.
    Equation for flight rocket is h(t) = -110t^2 + 2009.3t + 0.9 where h(t) is the height in meters above the ground after t seconds.

    What is the practical domain of the function. Explain your answear.
    Does the model seem realistic. Justify

    Quote Originally Posted by earboth at 9:52pm yesterday View Post
    1. Do yourself and do us a favour: If you have a new problem please start a new thread. Otherwise no member of the forum can see that you need some help.
    [0, \, t_1], where h(t_1) = 0 contains the clues to the answers for both the first and second part ......

    The last part is best left for you to further contemplate .....
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  5. #5
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    practical domain shouldn't be 0=<t=<18.23 ???
    18.23 is a root
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