t06 ⊾ ⊿ Name:

  1. __________ A ball bounce function is given by f(x)=100×0.85x 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)= 100×0.85x where x is the bounce number and f(x) is the bounce height. Solve for the bounce number x where f(x) is 8.73542 centimeters high .
  3. __________ The compound interest formula is given by: A=P (1+rn) nt For a principal P of $460, an interest rate r of 0.07, compounded n = 4 times a year, calculate the Amount A after a time t of nineteen years.
  4. __________ The continously compounding interest formula is given by: A=P e rt For a principal P of $460, an interest rate r of 0.05, calculate the Amount A after a time t of ten years.
  5. Transit Transit has a growth rate given by the following table:
    Age in months
    post-conception
    Actual mass
    in kilograms
    9.0 3.35
    10.24.69
    11.35.97
    13.27.59
    15.38.13
    21.79.29
    33.710.91

    Enter the data in a LibreOffice.org Calc spreadsheet. Insert a logarithmic trend line and show the equation. Write the equation below:


  6. ___________ Transit has a growth rate curve given by the equation above. Use the logarithmic equation to predict the mass of the baby at 27 months post-conception.
  7. __________ Transit 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 10 kilograms.
  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.

    __________ 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 2011?
  9. __________ How many years after 1954 until there is only 1 kilogram of the original 100 kilograms of Cesium-137 left in the soil?

    The circle has a radius r = 100. The shape is a seven sided heptagon. The center of the circle is (100,100). The coordinate system is SVG with y values increasing as one moves down the page. θ is theta. φ is phi.
    Heptagon 0 50 100 150 200 +x → 0 50 100 150 200 +y (0, 0) (100, 100) (200, 200) θ: 38.57° A B: adjacent C: coordinate D: opposite E: coordinate F: adjacent G: coordinate H: opposite I: coordinate φ 25.71° J K r = 100 r = 100
  10. ( _____ , _____ ) What are the coordinates of A, the point at the very top of the seven-sided heptagon?
  11. __________ Given r = 100 and θ = 38.57°, calculate the length of B, the adjacent side.
  12. ( _____ , _____ ) What are the coordinates of point C?
  13. __________ Given r = 100 and θ = 38.57°, calculate the length of D, the opposite side.
  14. ( _____ , _____ ) What are the coordinates of point E?
  15. __________ Given r = 100 and φ = 25.71°, calculate the length of F, the adjacent side.
  16. ( _____ , _____ ) What are the coordinates of point G?
  17. __________ Given r = 100 and φ = 25.71°, calculate the length of H, the opposite side.
  18. ( _____ , _____ ) What are the coordinates of point I?
  19. 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 8 cm 40 cm x RipStik rider

    λ = _______________ Determine the wavelength λ of the RipStik swizzle wave.
  20. a = _______________ Determine the amplitude a of the RipStik swizzle wave.
  21. f(x) = ______ sin( _________ x). Given the general form f(x)= asin( 2πx λ ) , write the equation for the RipStik swizzle wave.
  22. ________ Calculate arcsin( 3 2 ) , report the result in degrees.
  23. Right triangle θ 140 x 221 __________ For a right triangle with an opposite side of length 140 and a hypotenuse of 221, find the angle θ in degrees.
  24. __________ For a right triangle with an opposite side of length 140 and a hypotenuse of 221, find the length of the adjacent side x.
  25. ______, _____ Find the other two numbers in a Pythagorean triple where one of the three numbers is 28.
  26. _________ The equation for a projectile is given by: distance = 2 v 2 sin(θ) cos(θ) 9.8
    For a velocity v of 28 m/s, and an angle of 45°, calculate the distance d.
  27. _________ Solve for the velocity v: 2 v 2 sin(40) cos(40) 9.8 = 10.0491 with the angles given in degrees.
  28. Solve: 49.4109 sin(x) cos(x) = 24.3301 for 0 < x < π/2.
    Report the angle x in radians for the solution between 0 and π/2. Find the answer in decimal radians, not in arctan form. If there is more than one answer, report both. Note that π/2 is also equal to 1.57.


  29. Wagon Lever arm label Lever arm distance d Distance traveled vector and label Distance traveled vector d Wagon body zero Handle Wagon body proper Wagon wheels Handle pivot Force arrow Force F θ
    __________ For a force F of 30 Newtons, a distance of travel d of 800 meters, and an angle theta θ of 35°, use the dot product to calculate the work done pulling a toy wagon with the handle held at that angle.
  30. __________ For a force F of 30 Newtons, a lever arm distance d of 0.4 meters, and an angle theta θ of 35°, use the cross product to calculate the torque on a toy wagon with the handle held at that angle.
  31. Solve: (x − 5)² + (y − 4)² = 49, (x + 5)² + (y + 4)² = 81 for x and y. List all real solutions. Keep only two decimal places!


  32. Unnamed shape for purposes of a test____________ Calculate the magnitude for the vector {696, 697}.
  33. ____________ Calculate the angle relative to the horizontal axis for the vector {696, 697}.
  34. ______________________ What is the name of the shape?