1.

In 1919, H. S. Reed and R. H. Holland published a paper on the growth of sunflowers. Included in the paper were the table and graph above, which show the height h, in centimeters, of a sunflower t days after the sunflower begins to grow. The function h, defined by h(t) = at + b , where a and b are constants, models the height, in centimeters, of the sunflower after t days of growth during a time period in which the growth is approximately linear. What does a represent?

Answer»

The predicted NUMBER of centimeters the sunflower grows each day during the period
The predicted height, in centimeters, of the sunflower at the beginning of the period
The predicted height, in centimeters, of the sunflower at the end of the period
The predicted total increase in the height of the sunflower, in centimeters, during the period

Solution :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 t = 0, and since h(0) = 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 the function is c days long, then the predicted height, in centimeters, of the sunflower at the end of the period is represented by ac + 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 h(c) − h(0) = (ac + b) − (a · 0 + b), which is equivalent to ac, not a.


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