4. Обчислити \( \log _{7} 98-\log _{7} 2 \). a) \( 2 ; \) б) \( 96 ; \) в) \( 49 ; \) г) \( \frac{1}{2} \) 5. Знайти \( x \), якщо \( \log _{7} x=3 \log _{7} 5 \). a) \( 15 ; \) б) \( 21 ; \) в) \( 243 ; \) г) 125

Find an equation for the hyperbola described. Graph the equation. Center at \( (-1,-7) ; \) focus at \( (-1,-10) ; \) vertex at \( (-1,-9) \) Write an equation for the hyperbola. \( \square-\square=1 \) (Type exact answers for each term, using fractions as needed.)

The function \( f(t)=60,000(2)^{\frac{1}{40}} \) gives the number of bacteria in a population \( t \) minutes after an initial observation. How much time, in minutes, does it take for the number of bacteria in the population to double?

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

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.)