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2006 SQA Higher Maths: paper 2 no.11: Decay Equation

2,631 views · Published 23 February 2015 · 9:07 · Indexed 20 September 2026

Channel: DLBmaths · 2015 · Education

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Using a decay equation to determine the age of an object.

Here two methods are given:

(1) The primary one is to find the age from the percentage.

(2)  The alternative is to find the percentage resulting from the target age.

NOTE:   Here I have followed the given marking scheme for the alternative method – I do not agree with it at all!
 
Method (1) required no understanding of the behavior of the equation or the nature of its graph. It requires the solution of an equation and the use of logarithms.

Method (2) requires an understanding of the behavior of the equation and the nature of its graph. It does not require solving an equation or the use of logarithms.
Since higher candidates are required to know that the form of the graph of y=exp(-x) is strictly decreasing, I would maintain that a lower y value automatically guarantees a higher x value. In which case the problem is solved with a quick insertion of a value into an expression and a comparison of the result. Obviously the markers did not wish to give all 5 marks for this, and so this marking scheme was concocted.

Instructional exercise consisting of question 11 from paper 2 of the 2006 SQA Higher Mathematics exam.
Set out in stages of 'try then check' the worked solution to each part of the question.
Including indications of where each mark is allocated, and the requirements for that mark, according to the marking scheme.

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