Question

This is similar to a problem in the textbook. After a foreign substance is introduced into the blood, the rate at which antibodies are made is modeled by f(t)=19t3t2+7 where f(t) is in thousands of antibodies per minute, and t is measured in minutes with 0≤t≤10. Assuming that there are no antibodies present at time t=0, find the total number of antibodies in the blood at the end of 10 minutes. Round your answer to two decimal places.

Answer 1

We will find the number of antibodies by integrating the function:

∫

f

0

f

′

(

t

)

=

∫

60

0

27

t

8

t

2

+

3

d

t

Integrating both sides we get:

f

=

27

16

ln

(

8

t

2

+

3

)

Now let us plug-in the bounds we get:

Explanation: