Question

Anthropologists have noticed that they can predict the height of a human being based on the length of their femur. The relationship between the person's height, HHH, in centimeters, and length of the femur, fff, in centimeters, can be modeled by the equation below.

Answer 1

The question is incomplete! Complete question along with answer and step by step explanation is provided below.

Question:

Anthropologists have noticed that they can predict the height of a human being based on the length of their femur. The relationship between the person's height, H, in centimeters, and length of the femur, f, in centimeters, can be modeled by the equation below.

H(f) = 4.95f + 72.898

The function is valid for femur lengths between 38.1 cm and 60.96 cm, inclusive.

a. Graph the function, and determine a reasonable domain and range.

b. Suppose a female's femur is 39.37 cm long. About how tall was she?

c. If an anthropologist estimates a female's height as 5 feet 11 inches, about how long is her femur?

Answer:

a. $domain = 38.1 \leq f \leq 60.96$

$range = 261.49 \leq H \leq 374.65$

b. $H(39.37) = 267.78 \: cm$

c. $f = 21.71 \: cm$

Step-by-step explanation:

The equation of the function is given by

$H(f) = 4.95f + 72.898$

a. Graph the function, and determine a reasonable domain and range.

The graph of the function is attached.

The domain of the function is given by

$domain = 38.1 \leq f \leq 60.96$

The range of the function is given by

$range = H(38.1) \leq H \leq H(60.96)$

Where

$H(38.1) = 4.95(38.1) +72.898 \\\\H(38.1) = 188.59 + 72.898 \\\\H(38.1) = 261.49 \: cm$

$H(60.96) = 4.95(60.96) +72.898 \\\\H(60.96) = 301.75 + 72.898 \\\\H(60.96) = 374.65 \: cm$

So, the range is

$range = 261.49 \leq H \leq 374.65$

b. Suppose a female's femur is 39.37 cm long. About how tall was she?

$H(39.37) = 4.95(39.37) +72.898 \\\\H(39.37) = 194.88 + 72.898 \\\\H(39.37) = 267.78 \: cm$

Therefore, she is 267.78 cm tall.

c. If an anthropologist estimates a female's height as 5 feet 11 inches, about how long is her femur?

Let us first convert 5 feet 11 inches into cm

1 feet = 12 inches

5 feet = 12*5 = 60 inches

60 inches + 11 inches = 71 inches

1 inch = 2.54 cm

71 inches = 71*2.54 = 180.34 cm

$H(f) = 4.95f +72.898 \\\\180.34 = 4.95f +72.898 \\\\4.95f = 180.34 -72.898 \\\\4.95f = 107.44\\\\f = \frac{107.44}{4.95} \\\\f = 21.71 \: cm$