The amount of airline fuel consumed by Southwest Airlines each year between 2004

Question

The amount of airline fuel consumed by Southwest Airlines each year between 2004 and 2008 can be modeled as

(t) = 0.009t2 + 0.12t + 1.19 billion gallons

where t is the number of years since 2004.†

(a) Calculate the amount of fuel consumed in 2006. (Round your answer to three decimal places.)
_____ billion gallons

(b) Use the algebraic method to develop a formula for the derivative of f.
f'(t) = _____ billion gallons per year

(c) How quickly was the amount of fuel used by Southwest Airlines changing in 2006? (Round your answer to three decimal places.)
_____ billion gallons per year

Interpret the result.

In 2006, the amount of fuel used by Southwest Airlines was increasing/decreasing by _____ billion gallons per year.

Explanation / Answer

given f(t) = 0.009t2 + 0.12t + 1.19

a) in 2004 , t=0

in 2006, t =2006-2004=2

amount of fuel consumed in 2006 =f(2) = 0.009*22 + 0.12*2 + 1.19

amount of fuel consumed in 2006 =f(2) =1.394 billion gallons

b)d/dx xn =nxn-1

f '(t) = 0.009*2t2-1 + 0.12*1 + 0

f '(t) = 0.018t+ 0.12

c) f '(2) = (0.018*2)+ 0.12

f '(2) =0.084

amount of fuel used by Southwest Airlines changing in 2006 at 0.084 billion gallons per year

In 2006, the amount of fuel used by Southwest Airlines was increasing by 0.084 billion gallons per year.

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