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.)

Below is the graph of \( y=x^{3} \) Transform it to make it the graph of \( y=2(x-4)^{3}+3 \)

Write the vector \( \mathbf{v} \) in terms of \( \mathbf{i} \) and j whose magnitude \( \|\mathbf{v}\| \) and direction angle \( \theta \) are given. \( |\mathbf{v}|=36, \theta=45^{\circ} \) \( \mathbf{v}=\square \) (Simplify your answer. Type an exact answer, using radicals as needed. Use integers or fractic your answer in the form ai + bj. Rationalize all denominators)

Find the unit vector that has the same direction as the vector \( v \). \[ v=13 \mathbf{i}-5 \mathbf{j} \] The unit vector that has the same direction as the vector \( v=13 \mathbf{i}-5 \mathbf{j} \) is (Simplify your answer, including any radicals. Type your answer in the form ai + bj. Us expression. Rationalize all denominators.)

What is the range of the exponential function \( y=-5.3^{x+2}-2 \) ? a) \( \{y / y>2\} \) b) \( \{y / y<-2\} \) c) \( \{y / y<2\} \) d) \( \{y / y<-5\} \)

Repondre: Lensemble de definition de la fonction f est \( D_{f}=\left[-\frac{1}{2}, 4[\cup] 4,+\infty[\right. \). L'image de 3 par la fonction f est \( -\sqrt{7} \) . L'ensemble des antécédents de 0 par la fonction f est \( \left\{-\frac{1}{2}\right\} \) Question 3 1) Pour déterminer l'ensemble de définition d'une fonction, on doit trouver les valeurs de \( \times \) pour lesquelles la fonction est définie.