Question

A country's daily oil production can be approximated by q(t)=0.011t2−0.6t+5.29 million barrels (8≤t≤13)

where t is the time in year since the start of 2000 At the start of 2010 the price of oil was $28 per year How fast was oil revenue changing at that time?
At the start of 2010 oil revenue is decreasing at millions of dollars per year.

Answer 1

The oil revenue was changing at a rate of -0.38 million barrels per year at the start of 2010.

Step-by-step explanation:

To find how fast oil revenue was changing at the start of 2010, we need to calculate the derivative of the oil production function, q(t). The derivative represents the rate of change of oil production with respect to time. Let's differentiate the function q(t) using the power rule:

q'(t) = (d/dt)(0.011t^2 - 0.6t + 5.29)

= 0.022t - 0.6

Now, we can substitute the value of t = 10 (since the start of 2010 is 10 years after the start of 2000) into the derivative to find the rate of change at that time:

q'(10) = 0.022(10) - 0.6 = 0.22 - 0.6 = -0.38

Therefore, the oil revenue was changing at a rate of -0.38 million barrels per year at the start of 2010.