The function fx27Vx 197 models the median height ffx in inch

The function f(x)-2.7Vx +19.7 models the median height, ffx), in inches, of boys who are x months of age. The graph of f is shown. Complete parts a through c. 20 40 60 Age (months) a. According to the model what is the median height of boys who are 48 months, or four years, old? Use a calculator. inches (Round to the nearest tenth as needed.) The actual median height for boys at 48 months is 40.3 inches. Does the model overestimate or underestimate the actual height? O Overestimates O Underestimates O None of the above By how much? inches (Round to the nearest tenth as needed.) b. Use the model to find the average rate of change, in inches per month, between birth and 10 months The average rate of change is inches per month.

Solution

Given that   

f(x) = 2.7 x^1/2 +19.7

a ) Given that

x = 48 months

then

  f(48) = 2.7(48)^1/2 +19.7

=( 2.7 x 6.93 ) +19.7

= 38.4 inches

Given that

Actual meadian height of boys at 48 months = 40.3 inches

Hence,

The model underestimate the actual height

that is 40.3 - 38.4 = 1.9 inches

b )

Average rate of change between birth and 10 months = f(10) - f(0) / b-a

f(10) = 2.7(10)^1/2 +19.7

= 28.24 inches

f(0) =  2.7(0)^1/2 +19.7

= 19.7 inches

f(10) - f(0) / b-a = (28.24 - 19.7) / (10 - 0)

= 0.854 inches for month

Average rate of change between birth and 10 months = 0.854 inches per month

c )

Average rate of change between 50 and 60 months = f(60) - f(50) / b-a

f(60) =  2.7(60)^1/2 +19.7

= 40.61 inches

f(50) =  2.7(50)^1/2 +19.7

= 38.79 inches

f(10) - f(0) / b-a = (40.69 - 38.79) / (60 - 50)

= 0.19 inches for month

Average rate of change between 50 and 60 months = 0.19 inches per month

Hense,

The average rate of change between 50 and 60 months is less than the average rate of change between birth and 10 months