Question

Crude oil Imports to one country from another for 2009-2013 could be approximated by the following model where t is time in years since the start of 2000,

(1) --33428001 - 1,000 thousand barrels per day (9 st s 13)
According to the model, approximately when were oil imports to the country greatest? HINT (See Example 1) (Round your answer to two decimal places.)
How many barrels per day were imported at that time? (Round your answer to two significant digits.)
thousand barrels

Answer 1

• Time = approximately mid 2012
• Oil import rate = 3600 barrels

Explanation:

Unclear part of the question

• I(t) = −35t² + 800t − 1,000 thousand barrels per day (9 ≤ t ≤ 13)
• According to the model, approximately when were oil imports to the country greatest? t = ?

Solution

Given the quadratic function

• The vertex of a quadratic function is found by a formula: x = -b/2a

As per given function:

• b = 800, a = -35

Then

• t = - 800/2*(-35) = 11.43 which is within given range of 9 ≤ t ≤ 13

This time is approximately mid 2012.

Considering this in the function, to get oil import rate for the same time:

• l(11.43) = -35*(11.43)² + 800*11.43 - 1000 = 3571.4285

Rounded to two significant figures, the greatest oil import rate was:

• 3600 barrels