Caladan is currently one of the world's fastest-growing countries. The exponential function \( f(x)=91(1.021)^{x} \) modefs the population of Caladan, \( f(x) \), in millions, \( x \) years after 1974. Using this exponential function and a calculator with a \( { }^{x} \) key or a \( \wedge \) key, answer the following questions. a. Substitute 0 for \( x \) and, without using a calculator, find Caladan's population in 1974. 91 million b. Substitute 26 for \( x \) and use your calculator to find Caladan's population in the year 2000 as predicted by this function.

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (0,-8) \) and \( (0,8) \); vertices at \( (0,3) \) and \( (0,-3) \)

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.)

Find the standard form of the equation of the hyperbola satisfying the given conditions. Foci at \( (-7,0) \) and \( (7,0) \); vertices at \( (3,0) \) and \( (-3,0) \)

Follow the seven step strategy to graph the following rational function. \( f(x)=\frac{6 x}{x-3} \) Find the horizontal asymptote(s). Select the correct choice below and, if necessary, fill in the answer box to complete your choice. A. The equation(s) of the horizontal asymptote(s) is/are (Type an equation. Use a comma to separate answers as needed.) B. There is no horizontal asymptote.

Find the magnitude and positive direction angle of the vector \( \langle 2,-2 \sqrt{3}\rangle \). The magnitude of the vector is (Simplify your answer.)