On Your Own 9. A bacteria population \( y \) after \( x \) days can be represented by an exponential function whose graph passes through \( (0,100) \) and \( (1,200) \). a. Write a function that represents the population. b. Find the population after 6 days. Does this bacteria population grow faster than the bacteria population in Example 5 ? Explain.

Sketch the graph of the exponential function \( g(x) = 3^{x-1} + 2 \), indicating its asymptote.

The population of a southern city follows the exponential law. Use this information to answer parts a and b . (a) If N is the population of the city and \( t \) is the time in years, express \( N \) as a function of t . \( \mathrm{N}(\mathrm{t})= \) (Type an expression using \( t \) as the variable and in terms of \( e \).) (b) If the population doubled in size over 14 months and the current population is 60,000 , what will the population be 4 years from now? The population will be approximately \( \square \) people. (Do not round until the final answer. Then round to the nearest whole number as needed.)

Find polar coordinates of the point that has rectangular coordinates \( (-5,5 \sqrt{3}) \). Write your answer using degrees. Polar coordinates: \( \left(\square, \square^{\circ}\right) \)

Graph the function \( f(x)=\left\{\begin{array}{cc}5 & \text { if } x<0 \\ -\frac{1}{2} x+2 & \text { if } 0 \leq x \leq 2 \\ 1 & \text { if } x>2\end{array}\right. \)

Convert the following to cartesion coordinates (1) \( \left(2, \frac{\pi}{4}\right) \)