Chapter 7 - Algebra: Graphs, Functions, and Linear Systems - 7.3 Systems of Linear Equations in Two Variables - Exercise Set 7.3 - Page 446: 63

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(a) Consider the information provided. If \[x\] denotes the number of weeks, then the function for average number of symptoms,\[y\], can be expressed as sum of symptoms reported at the beginning of the semester and product of symptoms per week and no. of weeks. The function can be shown as follows for procrastinator students: \[y=0.8+0.45x\] Thus, the obtained function is \[y=0.8+0.45x\]. The function for average number of symptoms,\[y\], after \[x\] can be expressed as \[y=0.8+0.45x\]. (b) Consider the information provided. If \[x\] denotes the number of weeks, then the function for average number of symptoms,\[y\], can be expressed as sum of symptoms reported at the beginning of the semester and product of symptoms per week and no. of weeks. The function can be shown as follows for non procrastinator students: \[y=2.6+0.15x\] Thus, the obtained function is \[y=2.6+0.15x\]. The function for average number of symptoms,\[y\], after \[x\] can be expressed as \[y=2.6+0.15x\]. (c) Consider the information provided. The week in which both groups report same number of symptoms of physical fitness can be found by equating the functions for both groups, which is shown as follows: \[\begin{align} & 0.8+0.45x=2.6+0.15x \\ & 0.3x=1.8 \\ & x=6 \end{align}\] The symptoms reported by each group can be calculated by substituting this value in the function for that group. The symptoms reported by non procrastinator students are \[\begin{align} & y=2.6+0.15\times 6 \\ & y=3.5 \\ \end{align}\] The symptoms reported by procrastinator students are \[\begin{align} & y=0.8+0.45x \\ & y=0.8+0.45\times 6 \\ & y=3.5 \\ \end{align}\] It is shown in the figure that there is an intersection of both the functions at week \[6\]. Both the groups show equal number of symptoms for week \[6\] and symptoms reported by both the groups for that week would be \[3.5\].