1. ## 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?

2. 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.

3. 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

4. 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

Originally Posted by earboth at 9:52pm yesterday
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.
$\displaystyle [0, \, t_1]$, where $\displaystyle h(t_1) = 0$ contains the clues to the answers for both the first and second part ......

The last part is best left for you to further contemplate .....

5. practical domain shouldn't be 0=<t=<18.23 ???
18.23 is a root