The function that model the percentage of females in the country who hold a degree t years since 2010 is:
[tex]F(t)=0.59t+29.54[/tex]
And the function that model the percentage of males in the country who hold a degree t years since 2010 is:
[tex]M(t)=0.42t+30.22[/tex]
Now, to find the year at which the % of males and females who hold a degree are the same, then you need to find F(t)=M(t), replace the functions and find t as follows:
[tex]\begin{gathered} F(t)=M(t) \\ 0.59t+29.54=0.42t+30.22 \\ \text{subtract 29.54 from both sides} \\ 0.59t+29.54-29.54=0.42t+30.22-29.54 \\ 0.59t=0.42t+0.68 \\ \text{Subtract 0.42t from both sides} \\ 0.59t-0.42t=0.42t-0.42t+0.68 \\ 0.17t=0.68 \\ \text{divide both sides by 0.17} \\ \frac{0.17t}{0.17}=\frac{0.68}{0.17} \\ \text{Simplify} \\ t=4 \end{gathered}[/tex]
Then, let's evaluate both functions at t=4 to check:
[tex]\begin{gathered} F(4)=0.59\times4+29.54=31.9 \\ M(4)=0.42\times4+30.22=31.9 \end{gathered}[/tex]
Thus, the year will be 2010+4=2014
