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The function f (x )equals 2.9 square root of x plus 20.1, models the median height, f(x), in inches, of boys who are x months of age and for girls the function is f (x )equals 3.1 square root of x plus 19. Use a calculator to find the median height for both a boy and a girl who is 24 months old. Repeat the process for a child 48 months old. The actual median height for boys 48 months old is 40.8 inches and 40.2 inches for girls 48 months old. Does the model overestimate or underestimate the actual median heights and by how much

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Answer:

Kindly check explanation

Step-by-step explanation:

Given the models for the median height of biys and giels:

BOY:

f(x) = 2.9√x + 20.1

GIRL:

f(x) = 3.1√x + 19

If x = 24 months

BOY:

HEIGHT = 2.9√24 + 20.1

= 2.9× 4.8989794 + 20.1

= 14.207040 + 20.1

= 34.307 inches

GIRL:

HEIGHT = 3.1√24 + 19

= 3.1 × 4.8989794 + 19

= 15.186836 + 19

= 34.1868 inches

If x = 48

Boy:

HEIGHT = 2.9√48 + 20.1

= 2.9× 6.9282032 + 20.1

= 20.091789 + 20.1

= 40.19 inches

Actual median height = 40.8

Hence, model underestimates by (40.80 - 40.19) = 0.61 inches

Girl:

HEIGHT = 3.1√48 + 19

= 3.1 × 6.9282032 + 19

= 21.477430 + 19

= 40.48 inches

Actual median height = 40.20

Hence, model overestimates by (40.48 - 40.20) = 0.28 inches

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