If (y=10+kt) is linear growth, what must be true about (k)?
Answer and explanation
Correct answer: \(k>0\)
In \(y=10+kt\), \(k\) is the rate of change, or slope, of \(y\) with respect to \(t\). For linear growth, \(y\) must increase as \(t\) increases, so \(k>0\) is necessary. If \(k<0\), the relation shows linear decay, while \(k=0\) makes \(y\) constant. Exam tip: In \(y=a+mt\), the sign of \(m\) indicates growth or decay.
Frequently asked questions
What is the correct answer to this question?
\(k>0\)
Why is this the correct answer?
In \(y=10+kt\), \(k\) is the rate of change, or slope, of \(y\) with respect to \(t\). For linear growth, \(y\) must increase as \(t\) increases, so \(k>0\) is necessary. If \(k<0\), the relation shows linear decay, while \(k=0\) makes \(y\) constant. Exam tip: In \(y=a+mt\), the sign of \(m\) indicates growth or 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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