MS 101 Alg & Trig test four ⬠ Name:

24 June 2011

1. __________ A ball bounce function is given by $f\left(x\right)=100\mathrm{\times }{0.8}^x$ where x is the bounce number and f(x) is the bounce height. Evaluate this function at x = 10 bounces.
2. __________ A ball bounce function is given by $f\left(x\right)=100\mathrm{\times }{0.8}^x$ where x is the bounce number and f(x) is the bounce height. Solve for the bounce number x where f(x) is 4.0354 centimeters high .
3. __________ For the function shown in the chart, evaluate the height of the 5th bounce.
   
4. Logaleen has a growth rate given by the following table:
   

   Age in months post-conception x)	Actual mass in kilograms (y)
   9	3.4
   10	4.1
   11	4.8
   12	5.4
   13	6.0
   14	6.5
   15	7.0
   16	7.4

   
   Enter the data in a LibreOffice.org Calc spreadsheet. Insert a logarithmic trendline and show the equation. Write the equation below:
   
   
   
5. ___________ Logaleen has a growth rate curve given by the equation above. Use the logarithmic equation to predict the mass of the baby at 20 months post-conception.
6. __________ Logaleen has a growth rate curve given by the equation above. Use the logarithmic equation to solve for the month in which the baby will have a mass of 14 kilograms.
7. 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.
   
   __________ If there are 100 kilograms of Cesium-137 in the soil now, how many kilograms will be in the soil in 60 years?
8. __________ How many years until 10 kilograms of the original 100 kilograms of Cesium-137 is left in the soil?
9. The circle has a radius r = 100. The center of the circle is (100,100).
   
   __________ Given r = 100 and θ = 18°, calculate the length of B, the adjacent side.
10. __________ Given r = 100 and θ = 18°, calculate the length of D, the opposite side.
11. __________ Given r = 100 and φ = 36°, calculate the length of F, the adjacent side.
12. __________ Given r = 100 and φ = 36°, calculate the length of H, the opposite side.
13. A RipStik was ridden across a wet cloth towel soaked in water with food color. The RipStik was then swizzled across a large sheet of presentation paper. The swizzle wave can be seen in the diagram below.
    
    
    λ = _______________ Determine the wavelength λ of the RipStik swizzle wave.
14. a = _______________ Determine the amplitude a of the RipStik swizzle wave.
15. f(x) = ______ sin( _________ x). Given the general form $f\left(x\right)=a\sin \left(\frac{2\pi x}{\lambda }\right)$, write the equation for the RipStik swizzle wave.
16. _________ A tuning fork has a frequency of 384 Hertz. Calculate the period for the tuning fork.
17. _________ Calculate the period for f(x) = 42 tan (1.2566 x)