Determine the possible smallest subinterval $"n"$ value considering the Composite Simpson Rule approximation of the definite integral ${\displaystyle \underset{1}{\overset{3}{}}}[(x+2{)}^4+e^x]dx$ within ${10}^{-1}$ accuracy.

a$)2$

b$)3$

c$)4$

d$)5$

e$)$ None of these