Math: a9084ca4

ID: a9084ca4

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

Comment: This is more of an application question than anything. You might have to do no work at all.

Method 1: The y-intercept of a graph is when x = 0. In the given formula, if x = 0, the exponent will make the base 1, since any value other than 0 to the power of 0 is 1. Of course, you must observe the order of operations and resolve the exponent before multiplying.

f(0) = 9,000(0.66)^(0)

f(0) = 9,000(1)

f(0) = 9,000

If, as the setup tells us, x is the number of years since 1997, then the year must be 1997 (0 years after 1997). Since the equation models the number of ads a company sent its clients in a given year after 1997, then it must be true that in 1997, the company sent its clients 9,000 ads. That is exactly what answer choice (D) says, so the correct answer is (D).

Method 2: To avoid annoying window resizing on Desmos, you might try 9 rather than 9,000 and think in terms of thousands.

The graph clearly shows a y-intercept of (0, 9). Once again, if x is the number of years after 1997, then the y-intercept represents year 0, or 1997 itself. Then, 9,000 must fit into the correct answer, and (B) cannot be correct, since the graph shows a decrease after year 0—9,000 would be the maximum, rather than the minimum, number of ads sent in a given year. The correct answer must be (D).

Method 3: Lean on the answer choices to disprove them. (A) and (B) both include the curious phrase during the 5 years, but that would require plugging in different values for x, not a single value of 0. Thus, these cannot be correct. You can eliminate (C) on the grounds that 1,708 is not a number that can be derived by plugging in 0 for x in the given equation. Put your calculator to use if you have to. (1,708 is a rounded value you would get by plugging in 4.) Logically, the correct answer must be (D).

Any of the above methods should prove quick and, most importantly, accurate. Nothing beats knowing you have the correct answer within a short amount of time. You will be setting yourself up for not just the question in front of you, but the next question as well (positive thinking = positive momentum).