Posted by **tan** on Tuesday, March 19, 2013 at 3:06am.

assume that during the first 3 minutes after a foreign substance is introduced into the blood,the rate R'(t) at which new antibodies are produced(in thousands of antibodies per minute) is given by R'(t)=t/(t^2+1) where t is in minutes.find the total quantity of new antibodies in the blood at the end of 3 minutes.

- calculus -
**drwls**, Tuesday, March 19, 2013 at 3:17am
dR/dt = t/(t^2+1)

Assume R = 0 at t = 0

R = integral of t dt/(t^2 + 1)

= (1/2)ln(t^2 + 1)

At t = 3 minutes, R = (1/2) ln(10) = 1.15

Since R is measured in thousands, the answer is 1150.

- calculus -
**tan**, Tuesday, March 19, 2013 at 8:16am
i don't understand this part:dt/(t^2 + 1)

= (1/2)ln(t^2 + 1)

- calculus -
**Steve**, Tuesday, March 19, 2013 at 11:18am
It's not dt/(t^2 + 1)

It is t dt/(t^2 + 1)

That is just (1/2) du/u if u=t^2+1. That's where the log comes from

## Answer This Question

## Related Questions

- Calculus - fter a foreign substance is introduced into the blood, the rate at ...
- AP Calculus AB - A traffic engineer monitors the rate at which cars enter a ...
- Science - 1. How do antibodies make antigens useless? (1 point) by attaching to ...
- BioChem - Please help with this question. Insulin, antibodies, enzymes and ...
- Math expression - If the customer uses more than 450 minutes the payment is $39....
- college chemistry - Calcium oxide (CaO), an important ingredient in cement, is ...
- Math - One phone company charges $12 per month plus $.05 per minute after the ...
- Caluculus - Can anyone help me with this problem? Suppose that during a ...
- science - I do not understand this question. I tried to answer it but I am ...
- How can blood type A donate to AB??? - From my understanding, blood type A has A...

More Related Questions