Question

The polynomial function M(t) = LaTeX: 0.5t^4+3.45t^3-96.65t^2+347.7t0.5 t 4 + 3.45 t 3 − 96.65 t 2 + 347.7 t can be used to estimate the number of milligrams of the pain relief medication ibuprofen in the bloodstream t hours after 400 mg of the medication has been taken.

Find the number of milligrams in the bloodstream at t = 0, 0.5, 1, 1.5, 2, 2.5, 3, 3.5 and so on in intervals of .5 up to 6 hours. Round the function values to the nearest tenth.

Answer 1

To find the number of milligrams of ibuprofen in the bloodstream at different time intervals, substitute the given values of t into the provided polynomial function M(t) = 0.5t^4 + 3.45t^3 - 96.65t^2 + 347.7t.

Step-by-step explanation:

To find the number of milligrams of ibuprofen in the bloodstream at different time intervals, we can substitute the given values of t into the polynomial function M(t) = 0.5t^4 + 3.45t^3 - 96.65t^2 + 347.7t.

Substituting t = 0 into the function, we get M(0) = 0.5(0)^4 + 3.45(0)^3 - 96.65(0)^2 + 347.7(0) = 0.

Similarly, for t = 0.5, 1, 1.5, 2, 2.5, 3, 3.5, we substitute the values into the function to get the corresponding values of M(t).

Rounding these function values to the nearest tenth, we can calculate the number of milligrams in the bloodstream at each time interval.