What is the range of \( f(x)=4^{x}+2 \) ? (Type your answer is. interval notation.)

The exponential model \( \mathrm{A}=612.2 e^{0.014 t} \) describes the population, A, of a country in millions, \( t \) years after 2003. Use the model to determine when the population of the country will be 724 million. The population of the country will be 724 million in (Round to the nearest year as needed.)

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{6 x}{x-3} \) Find the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation(s) of the horizontal asymptote(s) is/are (Type an equation. Use a comma to separate answers as needed.) B. There is no horizontal asymptote.

Write the complex number in trigonometric form \( r(\cos \theta+i \sin \theta) \), with \( \theta \) in the interval \( \left[0^{\circ}, 360^{\circ}\right) \). \[ -3 \sqrt{3}+3 i \] \( -3 \sqrt{3}+3 i=\square\left(\cos \square^{\circ}+i \sin \square^{\circ}\right) \) (Type the value for \( r \) as an exact answer, using radicals as needed. Type the value for \( \theta \) as an intege as needed.)

Write the complex number in trigonometric form \( r(\cos \theta+i \sin \theta) \), with \( \theta \) in the interval \( \left[0^{\circ}, 360^{\circ}\right) \). \[ \begin{array}{l}1+i\end{array} \] \( \begin{array}{l}1+i=\square\left(\cos \square^{\circ}+i \sin \square^{\circ}\right) \\ \text { (Type the value for } r \text { as an exact answer, using radicals as needed. Type the value for } \theta \text { as an integer or } \\ \text { as needed.) }\end{array} \)

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (0,-8) \) and \( (0,8) \); vertices at \( (0,3) \) and \( (0,-3) \)