Question

From the beginning of 2007 to beginning of 2014, gasoline was consumed as a rate of q(t)=-1.2t+142 billion gallons per year (0 is less than or equal to t while t is also less than or equal to 7) with t being the number of years since 2007. During that same period of time, the price for gasoline was about p(t)=3.5-2.38e^(-0.5t) dollars per gallon. How do I use integrals to estimate to the nearest 10 billion dollars what the total amount of money spent on gasoline was during 2007-2014?

Answer 1

money spent is quantity * price, right?
So, for the 7-year period in question, that would be ∫[0,7] q(t)*p(t) dt
= ∫[0,7] (-1.2t+142)(3.5-2.38e^(-0.5t)) dt = 2730.46 $B