Chapter 6.3, Problem 5E

Reminder Round all answers to two decimal places unless otherwise indicated.

Deaths from the Heart Disease Table A and B show the deaths per $100,000$ caused by heart disease in the United States for males and females aged 55 to 64 years. The function $H_m$ gives deaths per $100,000$ for males, and $H_f$ gives deaths per $100,000$ for females.

a. Approximate the value of $\frac{d{H}_m}{dt}$ in 2004 using the average rate of change from 2004 to 2007.

b. Explain the meaning of the number you calculated in part a in practical terms. You should, among other things, tell what the sign means.

TABLE A Heart Disease Deaths per $100,000$

for Males Aged 55 to 64 Years

$t=\text{year}$	$H_m=\text{deaths per 100,000}$
$1990$	$537.3$
$2000$	$371.7$
$2003$	$331.7$
$2004$	$312.8$
$2007$	$288.8$

c. Use your answer from part a to estimate the heart disease death rate for males aged 55 to 64 years in 2006

d. Approximate the value of $\frac{d{H}_f}{dt}$ for 2004 using the average rate of change from 2004 to 2007.

e. Explain what your calculations from parts a and d tell you about comparing heart disease deaths for men and women in 2004.

TABLE B Heart Disease Deaths per $100,000$

for Females Aged 55 to 64 Years

$t=\text{year}$	$H_f=\text{deaths per 100,000}$
$1990$	$215.7$
$2000$	$159.3$
$2003$	$141.9$
$2004$	$131.5$
$2007$	$117.9$