91Ó°ÊÓ

Given the inequality, \(0.552 x^{3}+4.13 x^{2}-1.84 x-3.5<6.7\) a. Write the inequality in the form \(f(x)<0\). b. Graph \(y=f(x)\) on a suitable viewing window. c. Use the Zero feature to approximate the real zeros of \(f(x)\). Round to 1 decimal place. d. Use the graph to approximate the solution set for the inequality \(f(x)<0\)

An engineer for a food manufacturer designs an aluminum container for a hot drink mix. The container is to be a right circular cylinder 5.5 in. in height. The surface area represents the amount of aluminum used and is given by \(S(r)=2 \pi r^{2}+11 \pi r,\) where \(r\) is the radius of the can. a. Graph the function \(y=S(r)\) and the line \(y=90\) on the viewing window [0,3,1] by [0,150,10] . b. Use the Intersect feature to determine point of intersection of \(y=S(r)\) and \(y=90\). c. Determine the restrictions on \(r\) so that the amount of aluminum used is at most \(90 \mathrm{in}^{2}\). Round to 1 decimal place.

The concentration \(C(t)\) (in \(\mathrm{ng} / \mathrm{mL}\) ) of a drug in the bloodstream \(t\) hours after ingestion is modeled by $$ C(t)=\frac{500 t}{t^{3}+100} $$ a. Graph the function \(y=C(t)\) and the line \(y=4\) on the window [0,32,4] by [0,15,3] . b. Use the Intersect feature to determine the point(s) of intersection of \(y=C(t)\) and \(y=4\). c. To avoid toxicity, a physician may give a second dose of the medicine once the concentration falls below \(4 \mathrm{ng} / \mathrm{mL}\) for increasing values of \(t\). Determine the times at which it is safe to give a second dose. Round to 1 decimal place.