Sat practice Test #8 Answer Explanations

Choice C is correct. It is assumed that the oil and gas production 
decreased at a constant rate. Therefore, the function f that best models 
the production t years after the year 2000 can be written as a linear 
function, f (t) = mt + b, where m is the rate of change of the oil and 
gas production and b is the oil and gas production, in millions of 
barrels, in the year 2000. Since there were 4 million barrels of oil and 
gas produced in 2000, b = 4. The rate of change, m, can be calculated 
as 4 − 1.9 
_ 
0 − 13 = −
2.1 
_ 
13 , which is equivalent to −
21 
_ 
130 , the rate of change in 
choice C.
Choices A and B are incorrect because each of these functions has a 
positive rate of change. Since the oil and gas production decreased 
over time, the rate of change must be negative. Choice D is incorrect. 
This model may result from misinterpreting 1.9 million barrels as the 
amount by which the production decreased.
QUESTION 14
Choice C is correct. The second equation of the system can be 
rewritten as y = 5x − 8. Substituting 5x − 8 for y in the first equation 
gives 5x − 8 = x 
2
+ 3x − 7. This equation can be solved as shown 
below:
 x 
2
+ 3x − 7 − 5x + 8 = 0
 x 
2
− 2x + 1 = 0
(x − 1)
2
= 0
 x = 1
Substituting 1 for x in the equation y = 5x − 8 gives y = −3. Therefore, 
(1, −3) is the only solution to the system of equations.
Choice A is incorrect. In the xy-plane, a parabola and a line can 
intersect at no more than two points. Since the graph of the first 
equation is a parabola and the graph of the second equation is a line, 
the system cannot have more than 2 solutions. Choice B is incorrect. 
There is a single ordered pair (x, y) that satisfies both equations of the 
system. Choice D is incorrect because the ordered pair (1, −3) satisfies 
both equations of the system.
QUESTION 15