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+0.000446 t3​, 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.)

(a)20.65 lbs.

(b)1.88 lbs/month.

Step-by-step explanation:

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

Where t is measured in months; and

w is measured in pounds.

(a)When the baby is 7 months

Approximate Weight,

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

(b) If

Rate of change,

At t=7 months

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

see explanation

step-by-step explanation:

since the sequence is geometric there is a common ratio r between consecutive terms, that is

r = 4 ÷ - 2 = - 2

r = - 8 ÷ 4 = - 2

r = 16 ÷ 8 = - 2

the next term - 13 must be incorrect as it should be - 32 for the sequence to be geometric.

the first 4 terms are therefore geometric with common ratio r = - 2