For the exponential function f , the value of f 0 is c , where c is a constant. Of

Question

For the exponential function f , the value of f 0 is c , where c is a constant. Of the following equations that define the function f , which equation shows the value of c as the coefficient or the base?

Accepted Answer

Choice B is correct. Each of the given choices is an equation of the form f x = a b x - k , where a , b , and k are constants. For an equation of this form, the coefficient, a , is equal to the value of the function when the exponent is equal to 0 , or when x = k . It follows that in the equation f x = 33 1.5 x , the coefficient, 33 , is equal to the value of f 0 . Substituting 0 for x in this equation yields f 0 = 33 1.5 0 , which is equivalent to f 0 = 33 1 , or f 0 = 33 . Thus, the value of c is 33 and the equation f x = 33 1.5 x shows the value of c as the coefficient. Choice A is incorrect. This equation shows the value of f - 1 , not f 0 , as the coefficient. Choice C is incorrect. This equation shows the value of f 1 , not f 0 , as the coefficient. Choice D is incorrect. This equation shows the value of f 2 , not f 0 , as the coefficient.

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