If F(t) = 72 − 8t, what is the magnitude of the decay rate?
Answer and explanation
Correct answer: 8
A linear function has the form F(t) = initial value + rate × t. Comparing F(t) = 72 − 8t with this form, the initial value is 72 and the rate is the coefficient of t, namely −8. The negative sign indicates that F decreases as t increases, so the signed decay rate is −8 units per time. However, the question asks for the magnitude, which means the nonnegative size of the rate: |−8| = 8. Therefore option A is correct. The value 72 is the starting amount, 64 is not the rate, and −8 would be the signed rate rather than its magnitude.
Frequently asked questions
What is the correct answer to this question?
8
Why is this the correct answer?
A linear function has the form F(t) = initial value + rate × t. Comparing F(t) = 72 − 8t with this form, the initial value is 72 and the rate is the coefficient of t, namely −8. The negative sign indicates that F decreases as t increases, so the signed decay rate is −8 units per time. However, the question asks for the magnitude, which means the nonnegative size of the rate: |−8| = 8. Therefore option A is correct. The value 72 is the starting amount, 64 is not the rate, and −8 would be the signed rate rather than its magnitude.
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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