Question 481250
f(x)=-0.1x^2 + 2x + 58, where x is the number of years since 1985 (x=0 for 1985)
a. According to this equation, what was the oil consumption in 1990?
1990 - 1985 = 5
set x = 5 and solve f(5)
f(x)=-0.1x^2 + 2x + 58
f(5)=-0.1(5)^2 + 2(5) + 58
f(5)=-0.1(25) + 10 + 58
f(5)= 65.5 million barrels
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b. Using this equation, the maximum oil consumption will occur in what year?
It would be the vertex.
x = -b/(2a)
x = -2/(2(-0.1))
x = -2/(-0.2)
x = 10
year:
1985 + 10 = 1995
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c. What is the maximum oil consumption?
set x = 10 solve for f(x)
f(x)=-0.1x^2 + 2x + 58
f(5)=-0.1(10)^2 + 2(10) + 58
f(5)=-0.1(100) + 20 + 58
f(5)= 68 million barrels
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d. Does this equation realistically describe oil in 2030? why or why not?
2030-1985 = 45
set x = 45 solve for f(x)
f(x)=-0.1x^2 + 2x + 58
f(5)=-0.1(45)^2 + 2(45) + 58
f(5)=-0.1(2025) + 90 + 58
f(5)=-54.5 million barrels
answer: NO, because the result is negative
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