The yearly rate of consumption of natural gas of the city of Toronto is trillion

Question

The yearly rate of consumption of natural gas of the city of Toronto is trillion cubic feet per year in the t years since 1980. How much natural gas did Toronto use from 1988 to 2000? Round to the nearest trillion cubic foot. From 1988 to 2000 the city of Toronto used 294. 73 trillion cubic feet of natural gas. From 1988 to 2000 the city of Toronto used 149. 87 trillion cubic feet of natural gas. From 1988 to 2000 the city of Toronto used 45.35 trillion cubic feet of natural gas. From 1988 to 2000 the city of Toronto used 187. 49 trillion cubic feet of natural gas.

Explanation / Answer

dC/dt=.75t+1.5e^(.02t)

Integrating both sides to find C we get

C(t)=.375.t^2+75.e^(.02t)+K where K is a constant

Natural gas toronto used from 1988 to 2000=|C(20)-C(8)|=

|.375.(20)^2+75.e^(.02*20)+K-(.375.(8)^2+75.e^(.02*8)+K)|

=149.87

b.

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