MS 101 Alg & Trig test four ⬠ Name:

  1. __________ A ball bounce function is given by f(x)=100×0.8x 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(x)= 100× 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.
    exponential decay of bounce of a superball
  4. Logaleen the baby Logaleen has a growth rate given by the following table:
    Age in months
    post-conception
    x)
    Actual mass
    in kilograms
    (y)
    93.4
    104.1
    114.8
    125.4
    136.0
    146.5
    157.0
    167.4

    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 (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.

    __________ 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).
    Pentagon 0 50 100 150 200 +x → 0 50 100 150 200 +y (0, 0) (100, 100) (200, 200) θ: 18° A B: adjacent C: coordinate D: opposite E: coordinate F: adjacent G: coordinate H: opposite I: coordinate φ 36° J K r = 100 r = 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.
    RipStik swizzle sine wave 10 cm 34 cm x RipStik rider

    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(x)= asin( 2πx λ ) , 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)