The price of a certain commodity in dollars per unit at time t (measured in weeks) is given by p = 20 - 3e^-2t - 6e^-t/3. What is the average price of the commodity over the 5-week period from (t = 0) to (t = 5)? (Round your answer to the nearest cent.) $ per unit
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This will give us the total price over the 5-week period. The integral of p from 0 to 5 is ∫(20 + 3e^(-2t) + 6e^(-t/3)) dt from 0 to 5. This integral can be broken down into three separate integrals: ∫20 dt from 0 to 5 + ∫3e^(-2t) dt from 0 to 5 + ∫6e^(-t/3) Show more…
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