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f(0) For the^- exponential function f,^- the value of 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? f(x) = 22(1.5)^x+1
Correct answer: B (parsed from the explanation — this source omits an answer key for this item)
Explanation
Choice B is correct. Each of the given choices is an equation of the form = x - k f^xh a^bh , 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 = =33 1.5 x 0, or when x k. It follows that in the equation f^xh ^ h , the coefficient, 33, is equal to the value of f^0h. Substituting 0 for x in this equation yields 0 =33 1.5 0 0 =33 1 0 =33 f^ h ^ h , which is equivalent to f^ h ^ h, or f^ h . Thus, the value of =33 1.5 x c is 33 and the equation f^xh ^ h shows the value of c as the coefficient. - Choice A is incorrect. This equation shows the value of f^ 1h, not f^0h, as the coefficient. Choice C is incorrect. This equation shows the value of f^1h, not f^0h, as the coefficient. Choice D is incorrect. This equation shows the value of f^2h, not f^0h, as the coefficient.
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