\( 1 \leftarrow \quad \begin{array}{l}\text { Caladan is currently one of the world's fastest-growing countries. The exponential function } f(x)=91(1.027)^{x} \text { models the } \\ \text { population of Caladan, } f(x) \text {, in millions, } x \text { years after 1974. Using this exponential function and a calculator with a } y^{x} \\ \text { key or } \mathrm{a}^{\wedge} \text { key, answer the following questions. } \\ \text { a. Substitute } 0 \text { for } x \text { and, without using a calculator, find Caladan's population in } 1974 \text {. } \\ \square \text { million }\end{array} \).

Find the magnitude and positive direction angle of the vector \( \langle 2,-2 \sqrt{3}\rangle \). The magnitude of the vector is (Simplify your answer.)

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.

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.)

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.)

2- Work out composite functions \( f \circ g \) and \( g \circ f \) for each of the following pairs of functions. \( \begin{array}{ll}\text { (a) } f(x)=x-1 \text { and } g(x)=x^{3} & \text { (b) } f(x)=\sqrt{x} \text { and } g(x)=x-2\end{array} \)