t07 ⊾ 18 July 2012 ⊿ Name:

1. f(x) = __________ What function best describes the number of ancestors in each generation n in the following genogram?
   
2. __________ Super ball bounce heights for a initial drop of 100 cm are described by the function:
   $f\left(x\right)=100e^{-0.223x}$ where x is the bounce number and f(x) is the bounce height. Solve for the bounce number x where the bounce height f(x) is 64 centimeters high.
3. Education: Learning curve data
   

   Attempt	Time (s)
   1	0
   5	8.54
   9	12.25
   16	16.58

   
   In February 2010 my daughter wanted to learn to ride a RipStik. Recognizing the opportunity to gather data, I timed each attempt she made to ride the RipStik. Her first time on the RipStik she fell off immediately - a ride of 0 seconds. By her fifth attempt she remained on the RipStik for 8.54 seconds. The data in the table above is selected from the first 16 attempts to ride the RipStik. Plot this data using a LibreOffice.org Calc spreadsheet. Add in a logarithmic trend line. Write the natural logarithmic trend line below. Round numbers to two decimal places:
   
   f(x) = _________ ln(x) + ____________
4. ____________ Use the logarithmic function to determine the riding time for the eighth attempt, x = 8. Round to two decimal places.
5. ____________ Use the logarithmic function to determine what attempt would be predicted to produce a ride time of 10 seconds, f(x) = 10. Report your answer to the nearest whole number.
6. Radioactive decay is given by:
   $N=N_o{e}^{-rt}$
   Where N_o is the initial amount of the radioactive material, r is the rate of radioactive decay, t is the time, and N is the amount left after time t. Polonium-210 is a highly radioactive substance. Polonium-210 has a half life of 138 days. After a time t of 138 days, an initial amount N_o of 100 nanograms will be an amount N of 50 nanograms. Use this information to solve for the radioactive decay rate constant r for Polonium-210.
   
   r = _________________
7. Suppose I want to inscribe a square inside a circle with a radius of 500. What will be the SVG coordinates of the four corners?
   
   A: ( ________ , _________ )
8. B: ( ________ , _________ )
9. C: ( ________ , _________ )
10. D: ( ________ , _________ )
11. d = _________ Depth charges are explosives that detonate at a specific depth d under the surface of the water. A destroyer armed with depth charges is using a sonar to determine the angle θ and the distance r to a submarine. If the angle θ = 40° and the range r is 156 meters, what is the value of the depth d?
    
12. On 27 June 2012 in SC 130 Physical science I swizzled a RipStik was swizzled across a length of paper in 1.23 seconds. The three swizzle waves on the paper can be seen in the diagram below.
    
    
    λ = _______________ Write the wavelength λ for one wavelength of the RipStik swizzle wave in centimeters.
13. a = _______________ Calculate the amplitude a of the RipStik swizzle wave.
14. τ = _______________ Calculate the period τ of the RipStik swizzle wave.
15. f = _______________ Calculate the frequency f of the RipStik swizzle wave.
16. b = _______________ Given that $b=\frac{2\pi }{\tau }$ , calculate b for the RipStik swizzle wave.
17. y = ______ sin( _________ x). Given the general form y = a sin(bx) and the results above, write the equation for the RipStik swizzle wave.
18. A Turkish F-4 Phantom II RC-4 is flying 23 kilometers off the coast of Syria. An anti-aircraft turret on the Syrian coast is tracking the Phantom. Determine the value the angle θ in degrees for a distance x of 20 kilometers along the coast.
    θ =
    
19. d = _________ Given a launch speed of v = 15 m/s, and a launch of 30°, determine the distance d a thrown ball would travel. The formula for the distance is:
    $d=\frac{2v^2\sin \left(\theta \right)\cos \left(\theta \right)}{\mathrm{9.8}}$
20. A system demonstrating harmonic motion will be demonstrated at the front of the classroom. The instructor will provide data based on measurements of the system. Write the trigonometric function for the periodic system using the sine function, your calculation of the amplitude, and your calculation of the period.
    f(x) = _______________ sin( ____________ t)
21. On a Thursday evening in July 2005 I was body board surfing in Malem. My total velocity v (speed) was the result of the vector addition of the velocity (speed) of the wave w and the velocity s of my board along the face of the wave. On that Thursday the waves were moving at a speed of:
    $\stackrel{\rightharpoonup }{w}=3i$ towards Malem and my board was moving at
    $\stackrel{\rightharpoonup }{s}=4j$ towards Lelu. Speed are in meters per second.
    Note that w and s are at right angles as shown in the inset diagram.
    
    Calculate my velocity v over the reef by adding the vectors w + s and reporting the magnitude of the resulting vector v: __________
22. __________ Calculate the angle between the total velocity vector v and wave velocity vector w.
23. 
    Do NOT try at home: Child towing a RipStik with a bicycle The bicycle provides a force of 100 Newtons at an angle of 20° to the horizontal. The RipStik generates a drag of 50 Newtons at an angle of 180° to the horizontal. What is the direction angle and magnitude of the net force on the RipStik? Add the two vectors to determine the resulting direction angle and magnitude of the net force.
    
    
    magnitude of net force: ____________
    
    direction angle in degrees of net force: ____________