
Lorenzo M.
asked 04/07/21Very confused on Calc 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)=14t/9t^2+5
where f(t) is in thousands of antibodies per minute, and t is measured in minutes with 0≤t≤120. Assuming that there are no antibodies present at time t=0, find the total number of antibodies in the blood at the end of 120 minutes. Round your answer to two decimal places.
Number of Antibodies (in thousands) =
2 Answers By Expert Tutors
This is a straightforward application of an integral: if we are given a rate of change function, as we are in this case, we integrate that function over a specific time interval to calculate the total change in the quantity. (In many cases, you need to remember to add that total change to the amount present at the beginning of the time interval. But in this case we are told that there are 0 antibodies present at t = 0, so when we calculate the integral, we have the total number present at t = 120.
So, use a calculator or online utility to find ∫0120 f(t)dt

Yefim S. answered 04/07/21
Math Tutor with Experience
f(120) = 14·120/(9·1202 + 5) = 0.13 = 130 antibodies
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Mark M.
Is "5" a part of the exponent?04/07/21