# Growth function

• Apr 17th 2008, 06:18 PM
Snowboarder
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?
• Apr 17th 2008, 10:18 PM
earboth
Quote:

Originally Posted by Snowboarder
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):

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

I take the first version.

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

Since $\displaystyle \lim_{t \mapsto \infty} A(t) = 3$ 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

$\displaystyle \frac{20+3t}{t+1}=5~\iff~20+3t=5t+5~\iff~15=2t ~\iff~t=\frac{15}2$ ... That means after 7½ weeks a worker has reached the state of a profi.
• Apr 18th 2008, 12:18 AM
Snowboarder
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
• Apr 18th 2008, 05:21 AM
mr fantastic
Quote:

Originally Posted by Snowboarder at 12:18am today
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

$\displaystyle [0, \, t_1]$, where $\displaystyle h(t_1) = 0$ contains the clues to the answers for both the first and second part ......