Use the formula \( t=\frac{\ln 2}{k} \) that gives the time for a population, with a growth rate \( k \), to double, to answer the following questions. The growth model \( \mathrm{A}=3 e^{0.007 t} \) describes the population, A , of a country in millions, \( t \) years after 2003 . a. What is the country's growth rate? b. How long will it take the country to double its population? \( \square \) years (Round to the nearest whole number.)

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

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

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

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

Find all vertical asymptotes of the following functio \[ f(x)=\frac{4 x^{2}-1}{6 x^{2}-15 x-9} \]