A research laboratory is developing a novel drug delivery system. They model the drug concentration in a patient’s bloodstream using a function $C(t)$, where $t$ is the time in hours since the drug was administered. The rate of change of the drug concentration is given by the function $C’(t) = rac{10t}{t^2 + 1} - e^{-t}$, where $C(t)$ is measured in mg/L.
c. Calculate the average rate of change of the drug concentration between $t = 1$ and $t = 3$ hours. Then, using the fundamental theorem of calculus, determine the change in drug concentration between $t=1$ and $t=3$ hours. Discuss how these two values relate to each other.
Marking your answer...
This may take a few seconds
Sign up for free to see your full marking breakdown and personalised study recommendations.
Create Free Account Log inThis is a free VCE Units 3 & 4 Mathematical Methods practice question worth 5 marks, testing your understanding of Anti-differentiation and Fundamental Theorem. It falls under Calculus in Unit 3: Mathematical Methods Unit 3. Submit your answer above to receive instant AI-powered marking and personalised feedback.
Extend introductory study of functions, algebra, calculus. Focus on functions, relations, graphs, algebra, and applications of derivatives.
Covers limits, continuity, differentiability, differentiation, and anti-differentiation.
anti-differentiation by recognition that $F^{\prime}(x)=f(x)$ implies $\int f(x) d x=F(x)+c$ and informal treatment of the fundamental theorem of calculus, $\int_{a}^{b} f(x) d x=F(b)-F(a)$
All free, all instant AI marking.
StudyPulse has thousands of VCE Mathematical Methods questions with full AI feedback, mark breakdowns, progress tracking, and study notes across every Key Knowledge point including Anti-differentiation and Fundamental Theorem.
