Name College Algebra Test 3 Spring 2024 Must show all required handwritten steps by you. No electronic devices are allowed except for a scientific calculator. 2_a\\3 1. Simplify: log, 81(';24) S W] (LAY 2. Find the domain: f(x) = log (5x + 3). Show inequality. Leave answer in interval notation form. 3. Let f(x)=5x*xand g(x) =4x?+ 2. Find (g f)(x) 4. Find the inverse function: f(x) =8x3 + 1 5. If $5000 is invested at 6% compounded continuously, how much will be in the account after two years? Show equation and steps to the answer. File preview 6. Solve for x (Show all steps including any substitutions): 22* 2* 12 =0 7. The half-life of carbon is 5730 years. If 50 grams is present now, how long will it take for 30 grams to be left? Show equation and steps how you solve it. State proper units. 8. Solve for x (Show all steps): loge(x + 5) + logeg(x) = 2 9. Solve for x: 8e%* + 5 =45 10. An object at temperature 96C is placed at a room at 16C. Four minutes later the temperature of the object is 45C. Use Newton's Law of Cooling to determine when the temperature of the object will reach 20C. Show all work. \fe equation of the parabola with focus at (-4,1) and directrix x = 4 14. Analyze the equation 9x* +4y\"> 18x+16y11=0 by doing the following. No work, no points. (a) Rewrite the equation in standard form (show every step clearly): File preview (b) Find the center: (c) Find the foci (ordered pairs in exact radical form): (d) Find the vertices: (e) The major axis is parallel to: (f) Graph