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.)

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

The average daily high temperature (in \( \left.{ }^{\circ} \mathrm{C}\right) \) in Karachi, Pakistan, on the \( t^{\text {th }} \) day of the year is approximately \( T(t)=29-5 \cos \left(\frac{2 \pi(t-12)}{365}\right) \). What are the highest and lowest average daily highs in Karachi? Give exact answers. Highest: \( \square{ }^{\circ} \mathrm{C} \) Lowest: \( \square{ }^{\circ} \mathrm{C} \)

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

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

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