Question

the median weight of a boy whose age is between 0 and 36 months can be approximated by the function w(t) = 8.72 + 1.31t - 0.0094t² + 0.000342t³, where t is measured in months and w is measured in pounds. use this approximation to find the following for a boy with median weight in parts a) through c) below. a) the rate of change of weight with respect to time w’(t) = 1.31 - 0.0188t + 0.001026t² b) the weight of the baby at age 13 months the approximate weight of the baby at age 13 months is \boxed{} lbs (round to two decimal places as needed.)

Explanation:

Step1: Substitute t = 13 into the weight function

The weight function is \( w(t) = 8.72 + 1.31t - 0.0094t^2 + 0.000342t^3 \). We substitute \( t = 13 \) into this function.
First, calculate each term:

• The constant term: \( 8.72 \)
• The term with \( t \): \( 1.31\times13 = 17.03 \)
• The term with \( t^2 \): \( - 0.0094\times13^2=-0.0094\times169=-1.5886 \)
• The term with \( t^3 \): \( 0.000342\times13^3 = 0.000342\times2197\approx0.751374 \)

Step2: Sum up all the terms

Now we sum up all these terms: \( w(13)=8.72 + 17.03- 1.5886 + 0.751374 \)
First, \( 8.72+17.03 = 25.75 \)
Then, \( 25.75-1.5886=24.1614 \)
Finally, \( 24.1614 + 0.751374=24.912774 \)

Step3: Round to two decimal places

Rounding \( 24.912774 \) to two decimal places gives \( 24.91 \) (since the third decimal place is 2, which is less than 5, we round down the second decimal place).

Answer:

\( 24.91 \)