Math: 16889ef3

ID: 16889ef3 

(SAT Suite Question Bank > Find Questions > Assessment: SAT + Test: Math + Domain: Algebra)

Comment: Put the two crucial pieces of information together to do as little work as possible.

Method 1: This is a pretty standard mathematical modeling question, and lines are often the easiest to work with. For our purposes, we can think of 4 million barrels as 4 and 1.9 million barrels as 1.9. If production decreased from 4 to 1.9 over 13 years, then we have a direct input-output relationship to test in the answer choices—13 years after the initial production of 4, the correct equation must churn out 1.9. Furthermore, it is not necessary to test answer choices (A) or (B), since they both show a positive slope, when a linear decrease should have a negative slope.

C. f(13) = -(21/130)(13) + 4 --> f(13) = -(21/10) + 4 --> f(13) = -2.1 + 4 --> f(13) = 1.9 √

To be honest, there is no need to go further. Eyeballing the equation in answer choice (D) allows us to deduce that the answer for f(13) would not be the same as the one above, so the equation cannot be correct. The correct answer must be (C).

Method 2: Plug in the equations to Desmos and graph. If you were unsure about the first two equations, you could enter all four answer choices one by one. Just use x for t. You can input y instead of f(x), but f(x) can be found in the "Add Item" menu, the big + right above the input lines (in the top-left corner of the image).

Just as we explored above, in method 1, the two upper lines have the wrong slope, and when x = 13, only the green line dips below 2. You can also click on the point x = 13 on that line, and a popup will show that y = 1.9, just what you want to see. The correct answer must be (C).

Method 3: You can fit the given information into y = mx + b form. The only catch is that the answer choices avoid decimals. Consider:

y = mx + b

y = mx + 4

m = (1.9 - 4)/(13 - 0) --> m = -2.1/13

y = -(2.1/13)x + 4

This is functionally equivalent to (C), which must be the correct answer.