The population of a particular city is increasing at a rate proportional to its size. It follows the function \( \mathrm{P}(\mathrm{t})=1+\mathrm{k} e^{0.09 \mathrm{t}} \) where k is a constant and t population is 23,000 , in how many years is the population expected to be 57,500 ? (Round to the nearest year.) A. 6 yr B. 10 yr C. 69 yr D. 4 yr

Determine the implied domain of the following function. Express your answer in interval notation. \[ f(x)=\sqrt{x}-9 \] Answer

Where is there a discontinuity / are there discontinuities (holes or asymptotes) in the rational function \( f(x)=\frac{x^{2}+3 x+2}{x^{2}-4} ? \) \( x= \) 0 \( x= \) 2 \( x= \) -2 \( x=2 \) -2 \( x=0 \) \( 2,-2 \) \( x \)

What is the magnitude of a vector with a horizontal component of 5 and a vertical component of \( 12 ? \)

The number of U.S. travelers to other countries during the period from 1990 through 2009 can be modeled by the polynomial function \( P(x)=-0.00530 x^{3}+0.1366 x^{2}+1.250 x+46.49 \) where \( x=0 \) represents \( 1990, x=1 \) represents 1991 , and so on and \( P(x) \) is in millions. Use this function to approximate the number of \( U \).S. travelers to other countries in each given year. (a) 1990 (b) 2000 (c) 2009 (a) In 1990 , the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.) (b) In 2000, the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.) (c) In 2009, the number of U.S. travelers to other countries was approximately \( \square \) million. (Simplify your answer. Type an integer or decimal rounded to the nearest tenth as needed.)

What is the direction of a vector with a horizontal component of 2 and a vertical component of -4 ?