Answer:
Part a: Saudi Arabia's daily oil revenue = $568.896
Part b: Rate of change in 2006 = 74.42%
Explanation:
Part a: Saudi Arabia's daily oil revenue:
Where t = 0, represents year 2000
2006 = t6
P(t) = 6t + 18 dollars per barrel (0 ≤ t ≤ 10)
Price for 2006:
Price in 2006 P(6) = 6(6) + 18 dollars per barrel (0 ≤ t ≤ 10)
Price in 2006 = 36 + 18 dollars per barrel (0 ≤ t ≤ 10)
Price in 2006 = $54 dollars per barrel (0 ≤ t ≤ 10)-------------(A)
Now we need to determine the quantity for 2006 to find the revenue:
Q(t) = −0.036t² + 0.62t + 8 million barrels per day (0 ≤ t ≤ 10)
Quantity for 2006 Q(6) = -0.036(6)² + 0.62(6) + 8 million barrels per day (0 ≤ t ≤ 10)
Q(6) = -1.2960 + 3.72 + 8 = 10.4240 barrels per day (0 ≤ t ≤ 10)--------(B)
To find daily oil revenue, we need to multiply the price of barrel to the quantity per day
Revenue in 2006 = A×B
Revenue in 2006 = $54 × 10.42.40
Revenue in 2006 = $562.896
Part b: Rate of change in 2006:
For this we need to compare the revenue in 2000 with 2006:
Price in 2000, where t=0
P(t) = 6t + 18 dollars per barrel (0 ≤ t ≤ 10)
P(0) = 6(0) + 18 dollars per barrel (0 ≤ t ≤ 10)
P(0) = $18 per barrel (0 ≤ t ≤ 10)
Price in 2000 = $18 per barrel (0 ≤ t ≤ 10)------- (C)
Quantity in 2000:
Q(t) =−0.036t² + 0.62t + 8 million barrels per day (0 ≤ t ≤ 10).
Q(0) = -0.036 (0)²+0.62(0) + 8 million barrels per day (0 ≤ t ≤ 10).
Q(0) = 8 million barrels per day (0 ≤ t ≤ 10).
Quantity in 2000 = 8 million barrels per day (0 ≤ t ≤ 10).------- (D)
Revenue in 2000 = Price in 2000 × Quantity in 2000
Revenue in 2000 = $18 × 8
Revenue in 2000 = $144
Rate of change = Revenue in 2006 - Revenue in 2000
Rate of change = $562.896 - $144
Rate of change = $418.896
Rate of change in percentage = (418.896/562.896)×100
Rate of change in percentage = 74.42%
