- ____________ Evaluate
for x = 3.
- ____________ Calculate: 12 log8(4).
- Rewrite 343 = 7x in logarithmic form and then solve for x.
- log19(x) = 2 in exponential form and then solve for x.
- Solve for x in the following equations:
____________
- ____________ 6 ln(6x) = 32.2517
- ____________
-
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
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.
- __________ 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?
- __________ How many years after 1954 until there is only 1 kilogram of the original 100 kilograms of Cesium-137 left in the soil?
-
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~abx1.
- a = ____________
- b = ____________
- _____________ Use the equation to predict the height of bounce number five.
-
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
- c = ____________
- d = ____________
- _____________ Use the equation to predict the coefficient of drag at 100 kilometers per hour.