Level 2 Calculus Walkthrough
Question 2(c)
2025 Paper — Rates of change and justifying when coffee was given
Question
Hemi is part of a student research project on how caffeine enters the bloodstream. A new device measures caffeine levels in his blood.
He is monitored for 180 minutes (3 hours) and, at some point, he is given a cup of coffee to drink.
\[
C(t)=\frac{t^3}{150}-1.4t^2+80t+240
\qquad
\{0 \le t \le 180\}
\]
\[
\text{where }C\text{ is the concentration }(\mu\text{g/L}),\text{ and }t\text{ is time in minutes.}
\]
\[
\text{(i) Show that the rate of change of concentration is }-16\text{ after }60\text{ minutes.}
\]
\[
\text{(ii) Use calculus to justify when Hemi was given the coffee.}
\]
Try the question yourself first. If you get stuck, open the hints before using the full walkthrough.
Differentiate first, evaluate the derivative at 60 for part (i), then use first and second derivatives together to identify the minimum turning point for part (ii).
Step 1
Differentiate \(C(t)\)
What is the rate-of-change function \(C'(t)\)?
Preview will appear here.