[tex]\bf \begin{cases}
f(t)=\cfrac{t^2}{9}\\\\
g(t)=e^{\cfrac{}{}\frac{-ln(t)}{4}}\\\\
k(t)=f(t)+c\cdot g(t)
\end{cases}\implies k(t)=\cfrac{t^2}{9}+C\cdot e^{\cfrac{}{}\frac{-ln(t)}{4}}
\\\\\\
k(1)=4\implies
\begin{cases}
k=4\\
t=1
\end{cases}\implies 4=\cfrac{1^2}{9}+C\cdot e^{\cfrac{}{}\frac{-ln(1)}{4}}
\\\\\\
4=\cfrac{1}{9}+C\cdot e^{\frac{0}{4}}\implies 4=\cfrac{1}{9}+C\cdot 1\implies 4-\cfrac{1}{9}=C
\\\\\\
\cfrac{35}{9}=C[/tex]
