Question

A model for the basal metabolism rate, in kcal/h, of a young man is given by the formula below, where t is the time in hours measured from 5:00 AM. What is the total basal metabolism of this man over a 24 hour period?R(t)=80-0.18cos πt/1224∫ R(t) dt=____?0

Answer 1

1920 k calories is the basal metabolism.

Explanation:

Formula to get the total basal metabolism has been given by the formula

R(t) =
`80-0.18cos(\pi t)/(12)`

Where t = time

Now to calculate the total basal metabolism we will integrate the function with respect to time from 0 to 24 hours.

`\int_(0)^(24)R(t)=\int_(0)^(24)(80-0.18cos(\pi t)/(12))dt`

=
`[80t-{0.18}* (sin(\pi t)/(12))/((\pi)/(12))]_(0)^(24)`

=
`[(80-0)24-(0.18* 12)/(\pi)(sin2\pi - sin0)]`

= [(80-0)24-(sin2\pi - sin0)]

= 80×24

= 1920 k calories

Therefore, 1920 k calories is the total basal metabolism of the young man.