The function h, defined by , 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?

In 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 correct answer is: The predicted number of centimeters the sunflower grows each day during the period

Step 1 of 2:
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 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  , and since  , the predicted height, in centimeters, of the sunflower at the beginning of the period is represented by b, not by a.
Step 2 of 2:
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 (c) - h(0) = (ac - b) - (a - 0 + b), which is equivalent to ac, not a.