1. ____________ Evaluate $f\left(x\right)=5^{2x-4}$ for x = 3.
2. ____________ Calculate: 12 log₈(4).
3. Rewrite 343 = 7^x 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:
   
   ____________ $4.90625=2{\left(\frac{5}{4}\right)}^x+1$
6. ____________ 6 ln(6x) = 32.2517
7. ____________ $e^{\left(\frac{x}{7}\right)}=1096.6332$
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
   $N=P{e}^{\left(-0.023t\right)}$ 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. A ball was dropped and the bounce heights for consecutive bounces were measured.
   

   x1	y1
   0	100
   1	80
   2	64
   3	51.2
   4	40.96

   
   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~ab^x₁.
   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.

    x2	y2
    23	0.49
    40	0.40
    47	0.20
    62	0.18
    123	0.20

    
    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.