Reversing a two-stage calibration
8 written marks
A sensor uses the calibration \(\displaystyle r= f(t)= \frac{3t+ 10}{4}\), where the permitted temperature \(t\) satisfies \(0\le t\le40\). The numerical reading \(r\) is dimensionless.
Part a · 2 marks
Find the range of permitted readings \(r\).
Part b · 3 marks
Express \(t\) in terms of \(r\). State the domain and range of this inverse calibration.
Part c · 3 marks
A second display shows \(s=2r-1\). Find the temperature corresponding to \(s=34\). Decide whether \(s=70\) can arise within the stated model.
Complete-answer checking, worked solutions and indicative written criteria.
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