Recall that if \( f(x)=a^{x} \), the following are true. \( \begin{array}{l}\text { - The graph of } g(x)=a^{-x}=f(-x) \text {, where } b>0 \text {, is obtained by reflecting the graph of } f \text { in the } y \text {-axis; } \\ \text { - The graph of } g(x)=-a^{x}=-f(x) \text {, where } b>0 \text {, is obtained by reflecting the graph of } f \text { in the } x \text {-axis. } \\ \text { - The graph of } g(x)=a^{x}+b=f(x)+b \text {, where } b>0 \text {, is obtained by shifting the graph of } f b \text { units upward. } \\ \text { - The graph of } g(x)=a^{x-b}=f(x-b) \text {, where } b>0 \text {, is obtained by shifting the graph of } f b \text { units to the right. } \\ \text { Determine the transformations for } g(x)=f(-x-5)=f(-(\square)) \text {. }\end{array} \) The graph of \( g \) can be obtained by reflecting the graph of \( f \) in the Select- then shifting \( f \square \)

Find the following product, and write the product in rectangular form, using exact values. \( \left[8\left(\cos 90^{\circ}+i \sin 90^{\circ}\right)\right]\left[3\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)\right] \) \( \left[8\left(\cos 90^{\circ}+i \sin 90^{\circ}\right)\right]\left[3\left(\cos 30^{\circ}+i \sin 30^{\circ}\right)\right]=\square \) \( ( \) Type your answer in the form \( \mathrm{a}+\mathrm{bi} \).

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

Suppose the half-life of a drug in the bloodstream is 9 hours. To the nearest milligram, how much of the drug is left in the bloodstream 20 hours after a 260 milligram dose? 56 milligrams 32 milligrams 190 milligrams 117 milligrams

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.)