For the function f , f 0 = 86 , and for each increase in x by 1 , the

Question

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 ?

Accepted Answer

The correct answer is 3.44 . It&rsquo;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 &#8722; 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&rsquo;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 &#8722; 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.

Question for-th