A certain tranquilizer decays exponentially in the bloodstream and has a half-life of 22 hours. How long with it take for the drug to decuy to \( 82 \% \) of the original dose? a) step 1 : Find \( K \) (Round to four decimalpleas) b) step 2 : Use \( k \) to determine how longlinhours) it will take for the drug to decay to \( 82 \% \) of the original dose. (Round to one decinalplace)

asymptotes of \( f \).

\( \lim _ { n \rightarrow + \infty } \frac { n ^ { 5 } + \sin n } { 3 ( \arctan n ) n ^ { 5 } } \)

MAS182 - Applied Mathematics 13. Final Examination - S1 2021 The water content \( W(t) \) (measured in grams) in the cheese is governed by the differential equation \[ \frac{d W}{d t}=-(W-100)^{2} \] with initial condition \( W(0)=200 \mathrm{~g} \) and time is measured in hours.

s] Using calculus and showing all working, graph the function \[ f(x)=\frac{x+2}{x^{2}-1} \]

5. [12 marks] Using calculus and showing all your working, sketch the function \[ f(x)=\frac{x}{x^{2}-4} \] noting the domain of \( f(x) \), any intercepts or asymptotes, symmetry, regions where the function is increasing or decreasing and any relative extrema. Note: You don't have to consider the second derivative and concavity.