Math: 84dd43f8

ID: 84dd43f8

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

Comment: Track what is left, not what is lost.

Method 1: If a function decreases by 80% for each increase in x by 1, then it will retain 20 percent of its value for each such increase. Thus, an increase of 2 would represent a retention of 0.2 * 0.2, or 0.04, 4 percent of the original value.

0.04 * 86 = 3.44

The correct answer is 3.44.

Method 2: It is probably best to use Desmos as a calculator, although you can trace the graph to find the correct answer. You have to think of how to set up the function, though. The general form for an exponential function is as follows: amount = starting value * (1.00 +/- percent as a decimal)^times compounded.

Whether you trace the graph itself or set up the same expression with the value 2 plugged in, you get the same result: the correct answer is 3.44.

Method 3: Shortcuts are great, but if you have trouble wrapping your head around why they work the way they do, you can always stagger the percentage decrease and figure out the correct answer step by step. As long as you do not have to go through a lot of steps (e.g., an exponent greater than 5), the question is not that bad with a calculator to do the arithmetic for you.

f(0) = 86

f(1) = 86 - 0.8(86)

f(1) = 86 - 68.8

f(1) = 17.2

f(2) = 17.2 - 0.8(17.2)

f(2) = 17.2 - 13.76

f(2) = 3.44

The correct answer is 3.44.