2 Eliminate the parameter of the plane curve described by the following parametric equations and describe the resulting graph. \[ 7(t)=\sqrt{2 t+4} \] \[ y(t)=2 t+1,-2 \leq t \leq 6 \]

Use transformations of the graph of \( y=x^{5} \) to graph the function. \( f(x)=(x-8)^{5}+6 \) Which tranformations are needed to graph the function? A. The graph of \( y=x^{5} \) should be horizontally shifted to the left by 6 units and shifted vertically down by 8 . B. The graph of \( y=x^{5} \) should be horizontally shifted to the right by 6 units and shifted vertically up by 8 . The graph of \( y=x^{5} \) should be horizontally shifted the the left by 8 units and shifted vertically down by 6 . D. The graph of \( y=x^{5} \) should be horizontally shifted to the right by 8 units and shifted vertically up by 6 .

\( 1 \leftarrow \) Use the formula \( t=\frac{\ln 2}{\mathrm{k}} \) that gives the time for a population, with a growth rate k, to double, to answer the following questions. The growth model \( \mathrm{A}=9 e^{0.005 t} \) describes the population, A , of a country in millions, t years after 2003. a. What is the country's growth rate? \( \square \% \) b. How long will it take the country to double its population? \( \square \) years (Round to the nearest whole number.)

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

The size of a certain insect population is given by \( \mathrm{P}(\mathrm{t})=400 e^{.03 \mathrm{t}} \), where t is measured in days. At what time will the population equal 1600 ?

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.)