The amount of trash G (t) , in tons per year, produced by a town is projected to continue growing according to the formula

Question

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.

Answer 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