The percent increase for in-state tuition at a certain public university during the years 1991 through 1999 can be modeled by the quadratic function defined by
$$f(x)=0.161 x^{2}-2.09 x+10.6$$
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 in 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?
A) (i) 25.1%;
(ii) 1997;
33.1%

B) (i) 7.1%;
(ii) 1996;
3)9%
C) (i) 5.8%;
(ii) 1996;
3.9%

D) (i) 4.8%;
(ii) 1995;
4.2%

Question

The percent increase for in-state tuition at a certain public university during the years 1991 through 1999 can be modeled by the quadratic function defined by
$$f(x)=0.161 x^{2}-2.09 x+10.6$$
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 in 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?
A) (i) 25.1%;
(ii) 1997;
33.1%

B) (i) 7.1%;
(ii) 1996;
3)9%
C) (i) 5.8%;
(ii) 1996;
3.9%

D) (i) 4.8%;
(ii) 1995;
4.2%

Quizplus · Accepted Answer

For (i), substitute $x = 3$ into the function to find the percent increase in 1993: $f(3) = 0.161(3)^2 - 2.09(3) + 10.6 = 5.8\%$. For (ii), find the vertex of the parabola, which gives the minimum point. The vertex $x$ value is $-b/(2a) = 6.49$, which rounds down to 1996. Substitute $x = 6$ into the function to find the percent increase: $f(6) = 3.9\%$.

The Percent Increase for In-State Tuition at a Certain Public f(x)=0.161x2−2.09x+10.6f(x)=0.161 x^{2}-2.09 x+10.6f(x)=0.161x2−2.09x+10.6

The Percent Increase for In-State Tuition at a Certain Public $f(x)=0.161 x^{2}-2.09 x+10.6$