Name: 1. Solve the following inequalities. Write your answer in interval notation and graph solution on a number line. Show all work. a) Sx+15 > 20 x-1 2 8 12 24 2. Solve the following equation. State any restrictions for x and if the equation is an identity, inconsistent, or conditional. Show all work. 1 6 12 x# The equation is x-3 x+9 x2+6x-27 3. Given g(x) = log3(x + 2) - 4, explain ALL transformations (in words) necessary to obtain the graph of g(x) from f (x) = log3X. (b) Sketch both functions, f (x)and g(x), using all transformations on f (x) on the graph provided. Show asymptotes for both functions. (c) Give the equation of the asymptote for g(x) 18 10 (d) State the domain and range of g(x) in interval notation Domain RangeName: 4. Solve the following equations. Give exact answers in terms of logarithms or natural logarithms. Show all work a) 7 + 3eox = 79 b) 322x+5 = 64x-3 5. Solve the following logarithmic equations. Give exact answers. Check your answers and reject any value of x that is not in the domain of the original equation. Show all steps. a)2 + 9 In(4x) = 83 b) Invx + 7 =3 c)log4 (x + 6) + log4(x + 3) = 1 6. Expand as much as possible. Simplify completely. There should be no exponents and no radicals in your final answer. Show all steps log 100000x5 Vx + 3 (x + 6)2Name: 7. Use the properties of logarithms to condense as much as possible. Write your final answer as a single logarithm, with a coefficient of one and as one fraction. Show all steps. [2 In(x - 9) - Inx - In (x2 - 81)] 8. Graph this system of inequalities. Shade the 10 * * solution region. (x2+ y2 5 25 xty 2 2 -10 -8 6 4 - 2 - 2+ -10 9. The logistic growth function f (t) = 1 128,000 1+4600e-t describes the number of people, f(t) who have become ill with influenza t weeks after its initial outbreak in a particular community. a) How many people became ill with the flu initially? b) How many people were ill by the end of the 4th week? c) What is the limiting size of the population that becomes ill?Name: 10. The half-life of a certain substance is 28 days. How long will it take for a sample of this substance to decay to 16% of its original amount? Round final answer to one decimal place. Use A = Apekt to solve. 1 1. Find the difference quotient - (*th)-f(x) h - for f (x) and simplify. f (x) = 3x2 + 4x - 8 12. How long will it take $15,600 to triple if it is invested in an account whose interest rate is 8% compounded continuously. Choose the correct formula, either A = P(1 + -)nit or A = Pert. Round your answer to the nearest tenth