Chapter 9.1, Problem 98E

(a)

To determine

To calculate:terms of the finite sequence

Answer to Problem 98E

  $\begin{array}{cc}n& p_n\\ 7& 37.8833\\ 8& 39.3992\\ 9& 40.2259\\ 10& 40.4\\ 11& 39.9581\\ 12& 38.9368\\ 13& 37.3727\\ 14& 35.3024\end{array}$

Explanation of Solution

Given information: $p_n=0.0061n^3-0.491n^2+7.85n+4.9,\text{and }n=7,8,\cdot \cdot \cdot ,14$

Calculation:For year $2007$ , $n=7$

  $\begin{array}{l}{p}_7=0.0061{\left(7\right)}^3-0.491{\left(7\right)}^2+7.85\left(7\right)+4.9\\ p_7=2.0923-24.059+54.95+4.9\\ p_7=37.8833\end{array}$

For year $2008$ , $n=8$

  $\begin{array}{l}{p}_8=0.0061{\left(8\right)}^3-0.491{\left(8\right)}^2+7.85\left(8\right)+4.9\\ p_8=3.1232-31.424+62.8+4.9\\ p_8=39.3992\end{array}$

For year $2009$ , $n=9$

  $\begin{array}{l}{p}_9=0.0061{\left(9\right)}^3-0.491{\left(9\right)}^2+7.85\left(9\right)+4.9\\ p_9=4.4469-39.771+70.65+4.9\\ p_9=40.2259\end{array}$

For year $2010$ , $n=10$

  $\begin{array}{l}{p}_{10}=0.0061{\left(10\right)}^3-0.491{\left(10\right)}^2+7.85\left(10\right)+4.9\\ p_{10}=6.1-49.1+78.5+4.9\\ p_{10}=40.4\end{array}$

For year $2011$ , $n=11$

  $\begin{array}{l}{p}_{11}=0.0061{\left(11\right)}^3-0.491{\left(11\right)}^2+7.85\left(11\right)+4.9\\ p_{11}=8.1191-59.411+86.35+4.9\\ p_{11}=39.9581\end{array}$

For year $2012$ , $n=12$

  $\begin{array}{l}{p}_{12}=0.0061{\left(12\right)}^3-0.491{\left(12\right)}^2+7.85\left(12\right)+4.9\\ p_{12}=10.5408-70.704+94.2+4.9\\ p_{12}=38.9368\end{array}$

For year $2013$ , $n=13$

  $\begin{array}{l}{p}_{13}=0.0061{\left(13\right)}^3-0.491{\left(13\right)}^2+7.85\left(13\right)+4.9\\ p_{13}=13.4017-82.979+102.05+4.9\\ p_{13}=37.3727\end{array}$

For year $2009$ , $n=14$

  $\begin{array}{l}{p}_{14}=0.0061{\left(14\right)}^3-0.491{\left(14\right)}^2+7.85\left(14\right)+4.9\\ p_{14}=16.7384-96.236+109.9+4.9\\ p_{14}=35.3024\end{array}$

The bar graph of the sequence from 7 to 14 i.e., year $2007$ to $2014$ is

  

(b)

To determine

To conclude:the result from bar graph

Explanation of Solution

Given information:

  

Calculation:

From bar graph, the height of bar increases till 2010. After 2010, the height of bar start decreases.

Percent $p_n$ of United States adults increases from 2007 to 2010 and start decreasing from 2011 to 2014.