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 - 0.0094t^2 + 0.000342t^3 ),
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 + 0.001026t^2 )

b) the weight of the baby at age 13 months
the approximate weight of the baby at age 13 months is 24.91 lbs
(round to two decimal places as needed.)

c) the rate of change of the baby’s weight with respect to time at age 13 months
the rate of change for the baby’s weight with respect to time at age 13 months is approximately (\boxed{quad}) lbs/month
(round to two decimal places as needed.)

Explanation:

Step1: Substitute t = 13 into w'(t)

We know that \( w'(t)=1.31 - 0.0188t+0.001026t^{2} \). Substitute \( t = 13 \) into this formula.
First, calculate each term:

• The first term is \( 1.31 \).
• The second term: \( - 0.0188\times13=-0.2444 \)
• The third term: \( 0.001026\times13^{2}=0.001026\times169 = 0.173394 \)

Step2: Sum up the terms

Now, sum the three terms: \( 1.31-0.2444 + 0.173394 \)
First, \( 1.31-0.2444=1.0656 \)
Then, \( 1.0656 + 0.173394=1.238994 \)

Step3: Round to two decimal places

Round \( 1.238994 \) to two decimal places. Looking at the third decimal place, which is 8, we round up the second decimal place. So \( 1.24 \) (since \( 1.238994\approx1.24 \) when rounded to two decimal places).

Answer:

1.24