Randall Model
Algebra 2 word problem?
Randall Curtain High School’s enrollment, E, decreased from 1955 to 1975. In 1975, the enrollment began to increase. For 1995 through 1995, the enrollment can be modeled by E=.37t^2 – 14.8t + 160 where t=5 corresponds to 1955. In what year was enrollment down to 300 students? Explain your answer algebraically and graphically.
Greetings,
300 = .37t^2 – 14.8t + 160
.37t^2 – 14.8t -140 = 0
From the quadratic formula
t = [14.8 +/- sqrt(14.8^2 + 4*.37*140)]/(2*.37)
t = 47.9 (only positive solution)
48 – 5 = 43 years after 1955
1955 + 43 = 1998
The graph is a parabola decreasing from t = 0, E =160 to t = 20 , E = 16 then inceasing again
E = 300 close to t = 48, which corresponds to the year 1998
Regards
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