Level 3 Integration Walkthrough
2018 NCEA Level 3 Integration Question 2(e)
2018 Paper
Question
The mass \(m\) grams of a burning candle \(t\) hours after it was first lit is modelled by
where \(k>0\) and \(m\ge10\). The candle initially had mass \(140\) grams. After three hours its mass had halved.
Find the time from when the candle was first lit for its mass to reduce to \(50\) grams.
You must use calculus and show the results of any integration needed to solve the problem.
First walkthrough idea
Focus to try first
Separate the variables to build the mass model, then use the two measured masses before solving for the target time.
Step 1
Separate and integrate
Move \(m-10\) to the left before integrating.
Show the first step’s working
Walkthrough overview
What this question practises
This 2018 walkthrough is part of AS91579 — Apply integration methods in solving problems.
Method: Solving and fitting an exponential candle-mass model.
This is Question 2(e) from the 2018 NCEA Level 3 Integration paper for AS91579 — Apply integration methods in solving problems. Use the guided hints to practise the method before revealing the full working.
Calc.nz is an independent learning resource. Compare questions, diagrams, and assessment information with the official NZQA resources for AS91579.
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Learning summary
Review the method, not only the answer
This walkthrough helps you practise solving and fitting an exponential candle-mass model. Use the hints to plan the method, then repeat the question without hints and check each step.
Common mistake to avoid
Check each step against the original condition, preserve signs and restrictions, and confirm that the final result answers the question asked.