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

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

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

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.)