Question

The median weight of a boy whose age is between 0 and 36 months can be approximated by the function w (t )equals 8.38 plus 1.51 t minus 0.0069 t squared plus 0.000254 t cubed​, 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.

Answer 1

Answer:

a) W'(t) = 1.51 -0.0138t + 0.000762t² pounds/day

Step-by-step explanation:

The median weight of a boy with age between 0 and 36 months is given by:

$W(t) = 8.38+1.51t-0.0069t^2 + 0.000254t^3$

To find the rate of change of weight with respect to time, that is, the change in weight measured in pounds caused by a unit change in time, measured in days, simply derivate the weight function over time:

$\frac{d(W(t)}{dt}= W'(t) = 1.51-0.0138t + 0.000762t^2$

The rate of change is 1.51 -0.0138t + 0.000762t² pounds/day.