Question 39353
Year Sales Tax Revenue 
2000 $19500
2001 $21000
2003 $24000
2004 $27300
2005 $31000
a) Using the two points defined by data from 2000 and 2005, develop a linear equation for the data.
2000 $19500 at this time (0 years from 2000)
2005 $31000 at this time (5 years from 2000)
y = ((31000-19500)/5)x + 19500
y = 2300x + 19500
b) Using the equation found in a), predict the tax revenue for 2006.
y = 2300(6) + 19500
y = 13800 + 19500 = 33300
c) Use the calculator to determine the "best fit" equation for the data.
I haven't done any equations dealing with the "best fit" line, but I will try my best. It seems right.
y = (31000-((19500 + 21000 + 24000 + 27300 + 31000)/5))x + 19500
y = 2205x + 19500
d) Using the equation found in c), predict the tax revenue for 2006.
y = 2205(6) + 19500 = 32730
e) Using the equation found in c), estimate tax revenue for the missing 2002 data
y = 2205x(2) + 19500 = 23910
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{{{f(x) = -0.0128x^2 + x + 60}}}
a) What is the maximum height attained by the rocket? How far has the rocket travelled horizontally at this point?
The highest point would be at the vertex.
((-b/2a),f(x))
10000/256 = 5000/128 = 2500/64 = 1250/32 = 625/16
f(x) = -0.0128(625/16)^2 + (625/16) + 60
v(39.0625,79.53125) Max height: 39.0625ft.  Distance traveled: 79.53125ft.
b) At waht point(s) (after launch) is the rocket 70 feet high? (Horizontal displacement)
{{{f(x) = -0.0128x^2 + x + 60}}}
{{{70 = -0.0128x^2 + x + 60}}}
{{{0 = -0.0128x^2 + x - 10}}}
Use the quadratic formula to determine the root.
*[invoke quadratic "x", "-.0128", 1, -10]
At about 11.8 ft. horizontally or about 66.4 ft.
c) How far away from the base of the cliff does the rocket land?
Again, use quadratic formula to determine the roots.
*[invoke quadratic "x", "-.0128", 1, 60]
At about 117.9 ft. horizontally.