We are asked to determine the rate of change of the values of vacation days between 2010 and 2011.
To do that we will use the following formula:
[tex]r=\frac{f(t_2)-f(t_1)}{t_2-t_1}[/tex]Where:
[tex]\begin{gathered} f(t_2),f(t_1)=\text{ vacation days for t2 and t1 respectively} \\ t_2,t_1=\text{ years in cosideration. } \end{gathered}[/tex]For the given case we have:
[tex]\begin{gathered} t_2=2011 \\ t_1=2010 \end{gathered}[/tex]The vacation days associated to each of the years are:
[tex]\begin{gathered} f(2010)=16 \\ f(2011)=25 \end{gathered}[/tex]Now, we plug in the values in the formula for rate of change:
[tex]r=\frac{25-16}{2011-2010}[/tex]Now, we solve the operations:
[tex]r=\frac{9}{1}=9[/tex]Therefore, the rate of change is 9 days per year.
