The price of a certain commodity in dollars/unit at time (measured in weeks) is given by What is the average price of the commodity over the 7-week period from to ? Round the answer to the nearest cent.
A) $4.15
B) $12.43
C) $7.92
D) $6.81
E) $10.14

Question

The price of a certain commodity in dollars/unit at time  (measured in weeks) is given by  What is the average price of the commodity over the 7-week period from  to  ? Round the answer to the nearest cent.
A) $4.15 
B) $12.43 
C) $7.92 
D) $6.81 
E) $10.14

Quizplus · Accepted Answer

To find the average price, we need to take the integral of the price function over the given time period and divide by the length of the time period.

∫[4,5] 4 + 2cos(πt/2) dt = (4t + 4sin(πt/2))/π |[4,5]

Using this formula and simplifying, we get:

[(20+4sin(5π/2))/π - (16+4sin(4π/2))/π]/(5-4)
= [20/π - 16/π]/1
= $1.273US

Rounding to the nearest cent, we get $7.92 which is answer C.

The Price of a Certain Commodity in Dollars/unit at Time