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# @CPhill

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Let the amount of cola consumed in the United States be given by K(t) = $$6x^2-8 \sqrt x +3$$ with K measured in billions of gallons per year and t is measured in years from the beginning of 1990. What is the average rate of consumption of cola over the 10 year time period beginning January 1, 1992?

a) 82.3604 billions of gallons per year

b) 839.29 billions of gallons per year

c) 57.67 billions of gallons per year

d) 823.604 billions of gallons per year

I'm very sorry if I'm bothering you :|

Mar 30, 2018

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+100571
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Don't worry....you're not bothering me...LOL!!!

We should have t  instead of   x  in the function

If  we let  1990  =  year "0".....then we can consider 1992 as  year "2"

And so....10 years after this is year "12"

So   we want to find this

[ Consumption in year 12  - Consumption in year 2 ]

__________________________________________

12   -  2

[  ( 6(12)^2 - 8√12 + 3)  - ( 6(2)^2 - 8√2 + 3 ) ]

____________________________________

10

[ (6(12)^2 - 8√12  - 6(2)^2  + 8√2 ]

___________________________

10

[ 864  - 8√12 + 8√2 - 24 ]

____________________

10

[ 840  - 8√12 + 8√2 ]

________________   ≈     82.36 billions per year  ⇒  Answer "a"

10

Mar 30, 2018