[Video] Q13: Oil and gas production in a certain area dropped from 4 million barrels in 2000 to 1.9 million barrels in 2013. assuming that the oil and gas production decreased at a constant rate, which of the following linear functions f best models the production, in millions of barrels, t years after the year 2000?

Explanation for Question 13 From the Math (No Calc) Section on the Official Sat Practice Test 8

So question number 13 is telling us about oil and gas production and how 2 it's dropped from 4 million to 1.9 million barrels. 3 And we can model this graphically. Let me get rid of some of this 4 extra stuff here. Okay. So we started at 4 million in 2000, 5 which tells us that we want to have a y-intercept of four because that's 6 our starting point, which makes sense as well as our, 7 in our answer choices, because all of them have a y-intercept before. 8 Now we can see that the number of barrels dropped over time, 9 right? So we want a negative slope. Now only C and D have negative 10 slopes, a and B have positive slopes, 11 so we can eliminate a and B. And now we just need to figure 12 out what is our slope. And we can do that by finding rise over 13 run. Now, rise is going to be the difference between our two data points, 14 which is 1.9 and four and four minus 1.9 gives us 2.1. 15 So that's going to be our numerator. And our denominator is a change in 16 our X value, our run. And since we're going from 2000 to 2013, 17 that's 13 years, we can see this is pretty similar to C. 18 So C might be right, but how do we get from 2.1 to 21? 19 And the reason is this decimal here inside of a fraction is kind of 20 ugly, right? Because we don't need a decimal. If we're using a fraction, 21 that's combining two things that kind of make the number a little more difficult 22 to work with. And we can get rid of this by multiplying 10 on 23 the top and the bottom of our fraction. Because when I multiplied by 10, 24 I can move this decimal point over. And then I get 21 instead 25 of 2.1, but I also get it over 130. 26 Cause I can't forget to move this decimal point over as well. 27 So since our slope is going to be negative 21, 28 over 130, our best answer is going to be C.