question 25 currently, italys yearly death rate exceeds its birth rate. also, yearly immigration numbers are…

question 25 currently, italys yearly death rate exceeds its birth rate. also, yearly immigration numbers are approximately the same as emigration numbers, so italys overall population is declining. suppose in the table below, p(t) represents the rate of decline in italys population each year in thousands of people per year. estimate the area between p(t) and the t axis. round answers to the nearest tenth when appropriate. t (years) 2005 2006 2007 2008 2009 2010 2011 p(t) (thousand people per yr) -101 -119 -135 -134 -118 -101 -98 find the left riemann sum approximation using six rectangles of equal width. thousand find the right riemann sum approximation using three rectangles of equal width. thousand these two approximations represent which concept? the average rate of change in italys population from 2005 to 2011 the approximate decrease in italys population from 2005 to 2011 the approximate increase in italys population 2005 to 2011

question 25 currently, italys yearly death rate exceeds its birth rate. also, yearly immigration numbers are approximately the same as emigration numbers, so italys overall population is declining. suppose in the table below, p(t) represents the rate of decline in italys population each year in thousands of people per year. estimate the area between p(t) and the t axis. round answers to the nearest tenth when appropriate. t (years) 2005 2006 2007 2008 2009 2010 2011 p(t) (thousand people per yr) -101 -119 -135 -134 -118 -101 -98 find the left riemann sum approximation using six rectangles of equal width. thousand find the right riemann sum approximation using three rectangles of equal width. thousand these two approximations represent which concept? the average rate of change in italys population from 2005 to 2011 the approximate decrease in italys population from 2005 to 2011 the approximate increase in italys population 2005 to 2011

Answer

Explanation:

Step1: Calculate width for left - Riemann sum

The time interval is from 2005 to 2011. For 6 rectangles, $\Delta t=\frac{2011 - 2005}{6}=1$.

Step2: Calculate left - Riemann sum

The left - Riemann sum $L_6=\sum_{i = 0}^{5}p(t_i)\Delta t$. Here, $t_0 = 2005,t_1=2006,t_2 = 2007,t_3=2008,t_4 = 2009,t_5=2010$ and $\Delta t = 1$. $L_6=p(2005)\times1 + p(2006)\times1+p(2007)\times1 + p(2008)\times1+p(2009)\times1 + p(2010)\times1$ $L_6=- 101-119 - 135-134-118-101=-608$.

Step3: Calculate width for right - Riemann sum

For 3 rectangles, $\Delta t=\frac{2011 - 2005}{3}=2$.

Step4: Calculate right - Riemann sum

The right - Riemann sum $R_3=\sum_{i = 1}^{3}p(t_i)\Delta t$. Here, $t_1 = 2007,t_2=2009,t_3 = 2011$ and $\Delta t = 2$. $R_3=p(2007)\times2 + p(2009)\times2+p(2011)\times2$ $R_3=(-135)\times2+(-118)\times2+(-98)\times2=-270 - 236-196=-702$.

Answer:

-608 -702 The approximate decrease in Italy's population from 2005 to 2011