1. (8 pts) (a) Convert x = 1 logs 3125 to exponential form. Show work. (b) Evaluate logs 3125 Do not use a calculator. Show work. 2. (8 pts) Evaluate log4100 to the nearest hundredth. Show work. 3. (8 pts) Expand log (14) and simplify as much as possible. Assume all quantities represent positive real numbers. Show work. 4. (8 pts) Use the properties of logarithms to write the expression as a single logarithm and, if possible, simplify. Show work. 5. 6. (1/4) logs (6x)-logs (y)-4 logs (w) (8 pts) Solve: 27x=. Do not use a calculator. Show work. 81' (12 pts) Solve: log 12(36-36x2)- log 12(1+x) = 2. Show work for solving and checking. 7. (5 pts) The home-ownership rate is the percentage of households that are owner-occupied. Based on data of U.S. home-ownership rates in the second half of the twentieth century, the following logarithmic model was determined: h(t) 375.2 In(t)-2815.4, where t year and h(t) = home-ownership rate, in percent. (Note that "In" refers to the natural log function) (no explanation required) Using the above model, what was the home-ownership rate in 1990, to the nearest tenth of a percent? Show work. 8. (10 pts) (a) If $6,000 is invested in an account which offers 4%, compounded monthly, find the amount in the account after 15 years. Show work. (b) If $6,000 is invested in an account which offers 4%, compounded continuously, find the amount in the account after 15 years. Show work. 9. (8 pts) Angle Conversion (a) Convert the angle 240 from degree measure into radian measure. Show work. (b) Convert the angle from radian measure into degree measure. Show work. 10. (13 pts) A cup of hot coffee was placed in a room maintained at a constant temperature of 69 degrees, and the coffee temperature was recorded periodically. t-Time C=Coffee Elapsed (minutes) Temperature (degrees F.) 0 166.0 Using exponential regression with the data set, the following temperature model was produced: C(t)=69+89.976 e-0.023 10 140.5 20 125.2 where Time Elapsed (minutes) 30 110.3 40 104.5 and C(t) Coffee Temperature (in degrees) at time f. 50 98.4 60 93.9 (a) Use the temperature model to estimate the coffee temperature C when 13 minutes have elapsed. Report your estimated temperature to the nearest tenth of a degree. Show work. (b) Suppose the coffee temperature C is 100 degrees. Solve an appropriate equation for to determine how much time has elapsed. Show algebraic work to solve the equation. Report your answer to the nearest tenth of a minute. (c) Briefly describe what happens to the coffee temperature C(t) as the elapsed time becomes larger and larger. Is this a realistic description of the behavior of the actual coffee temperature? 11. (12 pts) (no explanation required) (a) For the angle 262, what is the associated quadrant? 11. (12 pts) (no explanation required) (a) For the angle 262, what is the associated quadrant? (b) State a positive angle and a negative angle which are coterminal with the angle 262. (c) For the angle, what is the associated quadrant? 5 (d) State a positive angle and a negative angle which are coterminal with the angle