For the function f, f(0) = 86, and for each increase in x by 1, the value of f(x) decreases by 80%. What is the value of f(2)?

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Key Explanation: The correct answer is 3.44. It’s given that f(0) = 86 and that for each increase in x by 1, the value of f(x) decreases by 80%. Because the output of the function decreases by a constant percentage for each 1-unit increase in the value of x, this relationship can be represented by an exponential function of the form f(x) = a(b) x , where a represents the initial value of the function and b represents the rate of decay, expressed as a decimal. Because f(0) = 86, the value of a must be 86. Because the value of f(x) decreases by 80% for each 1-unit increase in x, the value of b must be (1 − 0.80), or 0.2. Therefore, the function f can be defined by f(x) = 86(0.2) x . Substituting 2 for x in this function yields f(2) = 86(0.2) 2 , which is equivalent to f(2) = 86(0.04), or f(2) = 3.44. Either 3.44 or 86/25 may be entered as the correct answer. Alternate approach: It’s given that f(0) = 86 and that for each increase in x by 1, the value of f(x) decreases by 80%. Therefore, when x = 1, the value of f(x) is (100 − 80)%, or 20%, of 86, which can be expressed as (0.20)(86). Since (0.20)(86) = 17.2, the value of f(1) is 17.2. Similarly, when x = 2, the value of f(x) is 20% of 17.2, which can be expressed as (0.20)(17.2). Since (0.20)(17.2) = 3.44, the value of f(2) is 3.44. Either 3.44 or 86/25 may be entered as the correct answer.

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