The accompanying table gives the number of reported deaths due to AIDS, during the t th year

Question:

The accompanying table gives the number of reported deaths due to AIDS, during the t th year after 1995, for the period 1995 to 2006. (Source: Centers for Disease Control and Prevention, National Center for HIV, STD, and TB Prevention.)


image


However, the table does not tell the complete story because many deaths actually due to AIDS go unreported or are attributed to other causes. Let D(t) be the function that gives the cumulative number of AIDS deaths at time t. Then the data in the table can be thought of as rates of change of D(t) at various times, that is, as mortality rates. For instance, the table tells us that in 1997 (t = 2), AIDS deaths were increasing at the rate of 22,245 per year.


a. Assuming that D(t) is differentiable, explain why the total number of AIDSdeaths N during the period 1995–2006 is given by the integral


image


b. Estimate N by using the data in the table together with the trapezoidal rule to approximate the integral in part (a).

Fantastic news! We've Found the answer you've been seeking!

Step by Step Answer:

Related Book For  book-img-for-question

Calculus For Business, Economics And The Social And Life Sciences

ISBN: 9780073532387

11th Brief Edition

Authors: Laurence Hoffmann, Gerald Bradley, David Sobecki, Michael Price

Question Posted: