Question

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 hours).

1) why do we only need to look at the interval 0 < t < 6?

Answer 1

• The model is only defined on the interval 0 < t < 6
• Outside that interval, the equation gives unreasonable values

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.