Question

The median weight of a boy whose age is between 0 and 36 months can be approximated by the function w(t)=7.42+1.92t−0.0074t2+0.000446t3​, 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 weight of the baby at age 7 months. The approximate weight of the baby at age 7 months is __________ lbs. (Round to two decimal places as needed.) b) The rate of change of the baby's weight with respect to time at age 7 months. The rate of change for the baby's weight with respect to time at age 7 months is approximately ________ lbs/month (Round to two decimal places as needed.)

Answer 1

(a)20.65 lbs.

(b)1.88 lbs/month.

Explanation:

The median weight of the boy can be approximated by the function:

`w(t)=7.42+1.92t-0.0074t^2+0.000446t^3`

Where t is measured in months; and

w is measured in pounds.

(a)When the baby is 7 months

Approximate Weight,

`w(7)=7.42+1.92(7)-0.0074(7)^2+0.000446(7)^3\\=20.65$ pounds (to two decimal places)`

The approximate weight of the baby at age 7 months is 20.65 lbs.

(b) If
`w(t)=7.42+1.92t-0.0074t^2+0.000446t^3`

Rate of change,
`w'(t)=1.92-0.0148t+0.001338t^2`

At t=7 months

`w'(7)=1.92-0.0148(7)+0.001338(7)^2\\w'(7)=1.88$ lbs/month`

The rate of change for the baby's weight with respect to time at age 7 months is approximately 1.88 lbs/month.