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

Time = approximately mid 2012Oil import rate = 3600 barrels

Step-by-step explanation:

Unclear part of the questionI(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

The average number of skiers in Lavilla are 1,600 skiers

Step-by-step explanation:

The number of skiers that come to Lavilla on average each week = 2,800 skiers

The number of days each skier stays in Lavilla = 4 days

The amount each skier spends in local restaurants daily = $40

According to Little's Law, we have;

L = λ·W

Where;

L = The average number of skiers in Lavilla

λ = The effective arrival rate of the skiers = 2,800 skiers per week arrive

W = The number of days each skier stays at Lavilla = 4 days = 4/7 week

The average number of skiers in Lavilla, 'L', is therefore, given as follows;

L = 2,800 skiers/weel × (4/7) week = 1,600 skiers

The average number of skiers in Lavilla, L = 1,600 skiers