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.

2. Originally Posted by tondie2
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