Chapter 8.2, Problem 80E

a.

To determine

To find: an arithmetic sequence (linear model) for the given data using the regression feature of a graphing utility.

Answer to Problem 80E

  $a_n=0.838n+10.62867$ .

Explanation of Solution

Given information: The table shows the number $a_n$ (in thousands) of master's degree in

the biological and biomedical science conferred in the U.S. from 2011 through 2016.

Year	Master’s degree conferred $a_n$ (in thousands)
2011	11.32
2012	12.42
2013	13.30
2014	13.96
2015	14.66
2016	15.71

Calculation:

Let n =1 represents the year 2011, so the above data can be written as:

Year n	Master’s degree conferred $a_n$ (in thousands)
1	11.32
2	12.42
3	13.30
4	13.96
5	14.66
6	15.71

Using the regression feature of a graphing utility, the arithmetic sequence (linear modal) for the above table data is:

  $a_n=0.838n+10.62867$ .

b.

To determine

To approximate: the numbers of master’s degrees conferred for the year 2011 through 2016 using the sequence from part (a).

Explanation of Solution

Given information: The sequence from part (a) is $a_n=0.838n+10.62867$ .

Calculation:

The numbers of master’s degrees conferred for the year 2011 through 2016 using the sequence $a_n=0.838n+10.62867$ is shown in below table.

Let n =1 represents the year 2011

Year	Master’s degree conferred $a_n=0.838n+10.62867$ (in thousands)
2011	11.46667
2012	12.30467
2013	13.14267
2014	13.98067
2015	14.81867
2016	15.65667

c.

To determine

To find: the total number of master’s degrees conferred for the year 2011 through 2016 using the sequence from part (a).

Answer to Problem 80E

Therefore, the total number of master’s degrees conferred for the year 2011 through 2016 is 81.37002 thousands.

Explanation of Solution

Given information: The sequence from part (a) is $a_n=0.838n+10.62867$ .

Calculation:

The numbers of master’s degrees conferred for the year 2011 through 2016 using the sequence $a_n=0.838n+10.62867$ is shown in below table.

Let n =1 represents the year 2011

Year	Master’s degree conferred $a_n=0.838n+10.62867$ (in thousands)
2011	11.46667
2012	12.30467
2013	13.14267
2014	13.98067
2015	14.81867
2016	15.65667

The total number of master’s degrees conferred for the year 2011 through 2016 using the sequence is :

11.46667+12.30467+13.14267+13.98067+14.81867+15.65667 =81.37002 thousands.

Therefore, the total number of master’s degrees conferred for the year 2011 through 2016 is 81.37002 thousands.