Which rule has initial value (96) and decay rate (12)?
Answer and explanation
Correct answer: \(y=96-12x\)
A linear rule has the form \(y=a+bx\), where \(a\) is the initial value. A decay rate of 12 means that the value decreases by 12 for every increase of 1 in \(x\), so the coefficient of \(x\) must be \(-12\). Therefore, the rule is \(y=96-12x\). The rule \(y=96+12x\) represents growth at a rate of 12, not decay. Exam tip: put \(x=0\) to check the initial value, and look for a negative slope for decay.
Frequently asked questions
What is the correct answer to this question?
\(y=96-12x\)
Why is this the correct answer?
A linear rule has the form \(y=a+bx\), where \(a\) is the initial value. A decay rate of 12 means that the value decreases by 12 for every increase of 1 in \(x\), so the coefficient of \(x\) must be \(-12\). Therefore, the rule is \(y=96-12x\). The rule \(y=96+12x\) represents growth at a rate of 12, not decay. Exam tip: put \(x=0\) to check the initial value, and look for a negative slope for decay.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear growth and decay.
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