Question 820960: The percent increase for in-state tuition at a certain public university during the years 1991 through 1999 can be modeled by quadratic function defined by
f(x) =0.156x^2-2.02x+10.2,
where x=1 represents 1991, x=2 represents 1992, and so on.
(i) based on this model, by what percent (to the nearest tenth) did tuition increase by 1993?
(ii) In what year was the minimum tuition increase? (round down to the nearest year.) To the nearest tenth, by what percent did tuition increase that year?
Answer by TimothyLamb(4379)   (Show Source):
You can put this solution on YOUR website! ---
f(x) = 0.156x^2 - 2.02x + 10.2
x = year - 1990
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year = 1993
x = 1993 - 1990
x = 3
f(3) = 0.156(9) - 2.02(3) + 10.2
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answer 1:
f(3) = 5.544%
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f(x) = 0.156x^2 - 2.02x + 10.2 = 0
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the above quadratic equation is in standard form, with a=0.156, b=-2.02, and c=10.2
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to solve the quadratic equation, by using the quadratic formula, copy and paste this:
0.156 -2.02 10.2
into this solver: https://sooeet.com/math/quadratic-equation-solver.php
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the quadratic vertex is a minimum at: ( x= 6.47435897, f(x)= 3.66089744 )
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x= 6.47435897
6.47435897 = year - 1990
year = 6.47435897 + 1990
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answer 2:
year = 1996
tuition increased by 3.7% in 1996
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