1. ____________ Evaluate f (x) =52x-4 for x = 3.
  2. ____________ Calculate: 12 log8(4).
  3. Rewrite 343 = 7x in logarithmic form and then solve for x.
  4. log19(x) = 2 in exponential form and then solve for x.
  5. Solve for x in the following equations:

    ____________ 4.90625 = 2 ( 5 4 ) x + 1
  6. ____________ 6 ln(6x) = 32.2517
  7. ____________ e ( x 7 ) = 1096.6332
  8. The soil on Bikini atoll in the Marshall Islands is contaminated by the radioactive element Cesium-137. Like all radioactive elements, Cesium-137 will eventually decay into non-radioactive elements. The rate of decay is an exponential decay given by the formula
    N=P e (0.023t) where P is the starting amount of Cesium in the soil in kilograms, t is the number of years, and N is the remaining amount of radioactive Cesium after that number of years.

    1. __________ If there were 100 kilograms of Cesium-137 in the soil in 1954 as a result of the Castle Bravo thermonuclear hydrogen bomb test, how many kilograms will be in the soil now in 2017?
    2. __________ How many years after 1954 until there is only 1 kilogram of the original 100 kilograms of Cesium-137 left in the soil?
  9. tennis ball bouncing A ball was dropped and the bounce heights for consecutive bounces were measured.
    x1y1
    0100
    180
    264
    351.2
    440.96

    where x1 is the number of bounces and y1 is the height of that bounce in centimeters. Make a table and use the regression y1~abx1.
    1. a = ____________
    2. b = ____________
    3. _____________ Use the equation to predict the height of bounce number five.
  10. Design specifications for the 2018 world cup soccer ball have yet to leak, and only a few photos of the ball have appeared. The ball is thought to behave like the 2014 world cup soccer ball, the Brazuca. Soccer balls have a coefficient of drag that changes with the speed, Note that the actual function for the coefficient of drag is far more complex than a logarithmic equation can model. The Brazuca. Photo by AFP
    x2 y2
    23 0.49
    40 0.40
    47 0.20
    62 0.18
    1230.20

    where x2 is the speed of the ball in kilometers per hour and y2 is the coefficient of drag.
    Use the regression y2~cln(x2)+d
    1. c = ____________
    2. d = ____________
    3. _____________ Use the equation to predict the coefficient of drag at 100 kilometers per hour.