The function f ( x ) = 3.1 x + 19 models the median height, f ( x ) , in inches, of girls who are x months of age. The graph of f is shown. a. According to the model, what is the median height of girls who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for girls at 48 months is 40.2 inches. Does the model overestimate or underestimate the actual height? By how much? b. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth. c. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (b)? How is this difference shown by the graph?
The function f ( x ) = 3.1 x + 19 models the median height, f ( x ) , in inches, of girls who are x months of age. The graph of f is shown. a. According to the model, what is the median height of girls who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for girls at 48 months is 40.2 inches. Does the model overestimate or underestimate the actual height? By how much? b. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth. c. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (b)? How is this difference shown by the graph?
Solution Summary: The author explains how the median height of girls is overestimated by underset_40.5 inches and the average rate of change between birth and 10 months.
The function
f
(
x
)
=
3.1
x
+
19
models the median height,
f
(
x
)
, in inches, of girls who are
x
months of age. The graph of
f
is shown.
a. According to the model, what is the median height of girls who are 48 months, or four years, old? Use a calculator and round to the nearest tenth of an inch. The actual median height for girls at 48 months is 40.2 inches. Does the model overestimate or underestimate the actual height? By how much?
b. Use the model to find the average rate of change, in inches per month, between birth and 10 months. Round to the nearest tenth.
c. Use the model to find the average rate of change, in inches per month, between 50 and 60 months. Round to the nearest tenth. How does this compare with your answer in part (b)? How is this difference shown by the graph?
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