Calculus

The amount of trash G (t) , in tons per year, produced by a town is projected to continue growing according to the formula
dG/d t = 80 + 4t
. Based on this projection, calculate the total amount of trash that will be produced over the next 5 years, with t = 0 corresponding to the present time.

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  1. if dG/d t = 80 + 4t , then
    G = 80t + 2t^2 + c

    when t = 0, G = c
    when t = 5, G = 80(5) + 2(25) + c

    trash produced = 400 + 50 + c - c = 450

    or

    ∫ (80 + 4t) dt from t = 0 to 5
    = [80t + 2t^2] from 0 to 5
    = ( 80(5) + 2(25) - 0)
    = 450

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