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.)

Given an equation for a hyperbola, write the asymptotes and graph the equation. \( \frac{(y+3)^{2}}{4}-\frac{(x+5)^{2}}{9}=1 \) Positive-slope asymptote: Negative-slope asymptote:

How can the graph of \( f(x)=-(x-5)^{2}+7 \) be obtained from the graph of \( y=x^{2} ? \)

Which of the following is an approximation to six decimal places for \( \log _{8} 634 \) ? (1 point) 3.102780 2.802089 6.452049 1.898999

domínio \( \frac{\arcsin (-x-4)}{\sqrt{-x}-2} \)

Both of these functions grow as \( x \) gets larger and larger. Which function eventually exceeds the other? \[ f(x)=6 x-4 \] \( g(x)=\left(\frac{9}{5}\right)^{x} \)