P(r)= 0.5t^4 + 3.45t^3  96.65t^2 + 347.7t, when 0 < t < 6 in this function above, P(t) is the amount of medication (in mg) in the blood stream at time t (in ho
Question
in this function above, P(t) is the amount of medication (in mg) in the blood stream at time t (in hours).
1) why do we only need to look at the interval 0 < t < 6?
1 Answer

1. User Answers sqdancefan
Answer:
 The model is only defined on the interval 0 < t < 6
 Outside that interval, the equation gives unreasonable values
Stepbystep explanation:
You want to know why we only need to look at the interval 0 < t < 6 when using P(t) = 0.5t^4 + 3.45t^3  96.65t^2 + 347.7t to model the amount of medicine in the bloodstream.
1) Reasonable Domain
First of all, the domain of the model is given as 0 < t < 6, so this is the only interval on which the model is defined.
A polynomial function can be evaluated for all values of the independent variable. However, it may only reasonably model a given relation over some subset of those values. Here, the given polynomial is negative for t < 0 and for t > 6, so the polynomial values make no sense there. (Medicine concentration cannot be negative.)
The polynomial values increase rapidly for t > 6.1, so do not reasonably model medicine concentration after it has already become zero.