SAT Mathematics Practice Test 6

Questions 32-34 refer to the following information.

Sunflower Growth

Day	Height (cm)
0	0.00
7	17.93
14	36.36
21	67.76
28	98.10
35	131.00
42	169.50
49	205.50
56	228.30
63	247.10
70	250.50
77	253.80
84	254.50

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.

Question : 34 of 58

Marks: +1, -0

The growth rate of the sunflower from day

14

to day

35

is nearly constant. On this interval, which of the following equations best models the height h, incentimeters, of the sunflower

t

days after it begins

$h=2.1t-15$
$h=4.5t-27$
$h=6.8t-12$
$h=13.2t-18$

Validate

Solution:

According to the table, the height of the sunflower is 36.36 cm on day 14 and 131.00 cm on day 35. Since the height of the sunflower between day 14 and day 35 changes at a nearly constant rate, the height of the sunflower increases by approximately

{131.00-36.36}/{35-14}≈4.5

cm per day. Therefore, the equation that models the height of the sunflower t days after it begins to grow is of the form

h=4.5t+b.

Any ordered pair

(t,h)

from the table between day 14 and day 35 can be used to estimate the value of b. For example, substituting the ordered pair

(14, 36.36)

for

(t,h)

into the equation

h=4.5t+b

gives

36.36=4.5(14)+b

. Solving this for b yields

b=−26.64

. Therefore, of the given choices, the equation

h=4.5t−27

best models the height h, in centimeters, of the sunflower t days after it begins to grow.
Choices A, C, and D are incorrect because the growth rates of the sunflower from day 14 to day 35 in these choices are significantly higher or lower than the true growth rate of the sunflower as shown in the graph or the table. These choices may result from considering time periods different from the period indicated in the question or from calculation errors.

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