Find all horizontal asymptotes of the following function \[ f(x)=\frac{2(2 x+3)(x+4)}{3(x-6)(x+4)} \]

Write the equation of the hyperbola \( 36 x^{2}-16 y^{2}+360 x-128 y+68=0 \) in standard form \[ \begin{array}{l}\text { Where: } \\ h=-5 \\ k=-4 \\ a=4 \\ \mathrm{a}=4)^{2} \\ b=\square\end{array} \]

The rat population in a major metropolitan city is given by the formula \( n(t)=29 e^{0.01 t} \) where \( t \) is measured in years since 1994 and \( n \) is measured in thousands. (a) What was the rat population in 1994? (b) What is the rat population going to be in the year 2009?

2. \( y=\left\{\begin{array}{ll}1, & \text { if } 0 \leq x<3 \\ 0, & \text { if } 3 \leq x<6 \\ -1, & \text { if } 6 \leq x<9 \\ -2, & \text { if } 9 \leq x<12\end{array}\right. \)

Sea \( f: R^{+} \longrightarrow R^{+} / f(x)=2 x^{2} \). ¿Es biyectiva

A city had a population of 5,682 at the begining of 1949 and has been growing at \( 5.2 \% \) per year since then. (a) Find the size of the city at the beginning of 1976 . Answer: \( \square \) (b) During what year will the population of the city reach \( 22,586,370 \) ? Answer: