SOLUTION: the variable interest rate on a student loan changes each july 1 based on the bank prime loan rate.For the years 1992-2007 this rate can be approximated by the model r(x)= -0.115x^

Question 1146849: the variable interest rate on a student loan changes each july 1 based on the bank prime loan rate.For the years 1992-2007 this rate can be approximated by the model r(x)= -0.115x^2+1.183x+5.623 where x is the number of years since 1992 and r is the interest rate as a percent
calculate the highest rate during this time period during which year was the interest rate the highest
use graph to estimate the rate in 2010 does the value seem reasonable?
Answer by greenestamps(13200) (Show Source): You can put this solution on YOUR website!

(1) Graph the equation on a graphing calculator.

(2) Find the maximum value of the function, and the x value which produces that maximum. 1992 plus the x value is the year in which the interest rate is highest.

(3) Evaluate the function for x = 18 (2010 is 18 years after 1992). The function value is negative there. Is that reasonable?

Note that the problem says the given function is only applicable for the years 1992-2007; so using it to estimate the interest rate in 2010 might not be valid. However, even for the year 2007 (x=15), the function value is negative; so the function is not realistic.
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