Rewrite the Cartesian equation \( y=7 x^{2} \) as a polar equation. \( r(\theta)=\square \) Preview Enter theta for \( \theta \) if needed.

(7) Eldominio de \( f(x)=\ln \left(x^{2}-16\right) \) es

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

4. Sketch the graph of \( f(x)=3 x-x^{2} \) and find a. the domain and range b. \( f(q) \) c. \( f\left(x^{2}\right) \) d. \( \frac{f(2+h)-f(2)}{h}, h \neq 0 \).

of the following: (1) \( z=\frac{1}{1+i \tan \theta} \)

possible In 2012 , the population of a city was 6.04 million. The exponential growth rate was \( 3.29 \% \) per year. a) Find the exponential growth function. b) Estimate the population of the city in 2018 . c) When will the population of the city be 10 million? d) Find the doubling time. a) The exponential growth function is \( \mathrm{P}(\mathrm{t})=\square \), where t is in terms of the number of years since 2012 and \( \mathrm{P}(\mathrm{t}) \) is the population in millions. (Type exponential notation with positive exponents. Do not simplify. Use integers or decimals for any numbers in the equation.) b) The population of the city in 2018 is \( \square \) million. (Round to one decimal place as needed.) c) The population of the city will be 10 million in about \( \square \) years after 2012 . (Round to one decimal place as needed.) d) The doubling time is about \( \square \) years. (Simplify your answer. Round to one decimal place as needed.)