#$1)(5$ pts$)$ For the four algorithms, each having $n$ inputs, the complexities for doing the same task are A: $n^{\frac{f}{l}},B$ : $nlo{g}_{l}n,C$:$n(lo{g}_{l}n{)}^2,$ and $D$:$\sqrt[f]{n}lo{g}_{f}n.$ Rank the algorithms in order of increasing efficiency.

Consider the following function.

$f(t)=\frac{l{e}^{0\mathrm{.}05t}}{e^{0\mathrm{.}05t}+f}$

Where, $f$ and $l$ are the number of letters in your first and last names respectively.

#$2)(5$ pts$)$ Write the domain of the function, and find the horizontal asymptotes, if any.

#$3)(4$ pts$)$ For the same function stated above, find the intervals of concavity on its domain. Sketch the function graph $(1$ pt$)$ based on your solution for this problem and the earlier problem.

f$=5,$ l$=5$