SAT Mathematics Practice Test 6

Based on the definition and contextual interpretation of the function h,when the value of t increases by 1, the height of the sunflower increases by a centimeters. Therefore, a represents the predicted amount, in centimeters, by which the sunflower grows each day during the period the function models.
Choice B is incorrect. In the given model, the beginning of the period corresponds to $\mathit{t}=0$, and since $\mathit{h}\left(0\right)=\mathit{b}$, the predicted height, in centimeters, of the sunflower at the beginning of the period is represented by b, not by a. Choice C is incorrect. If the period of time modeled by thefunction is c days long, then the predicted height, in centimeters, of the sunflower at the end of the period is represented by $\mathit{a}\mathit{c}+\mathit{b}$, not by a. Choice D is incorrect. If the period of time modeled by the function is c days long, the predicted total increase in the height of the sunflower, in centimeters, during that period is represented by the difference $\mathit{h}\left(\mathit{c}\right)-\mathit{h}\left(0\right)=\left(\mathit{a}\mathit{c}+\mathit{b}\right)-\left(\mathit{a}·0+\mathit{b}\right)$, which is equivalent to ac, not a.