If D(t) = 72 − 9t, by how much will D(t) decrease when t increases by 1?
Answer and explanation
Correct answer: 9
The governing concept is the constant rate of change in a linear expression. In D(t) = 72 − 9t, the coefficient of t is −9, so increasing t by 1 changes the value by −9. This means the value itself decreases by 9 units; the word “decrease” asks for the positive size of the reduction, namely 9. Directly, D(t + 1) = 72 − 9(t + 1) = 72 − 9t − 9 = D(t) − 9. Therefore, option A is correct. The value −9 describes the signed change, while 72 is the initial constant and 63 is not the change for an arbitrary t.
Frequently asked questions
What is the correct answer to this question?
9
Why is this the correct answer?
The governing concept is the constant rate of change in a linear expression. In D(t) = 72 − 9t, the coefficient of t is −9, so increasing t by 1 changes the value by −9. This means the value itself decreases by 9 units; the word “decrease” asks for the positive size of the reduction, namely 9. Directly, D(t + 1) = 72 − 9(t + 1) = 72 − 9t − 9 = D(t) − 9. Therefore, option A is correct. The value −9 describes the signed change, while 72 is the initial constant and 63 is not the change for an arbitrary t.
Which subject and chapter does this question cover?
This is a Class 9 Mathematics question. Chapter: Introduction to Polynomials. Topic: Linear growth and decay.
Student feedback
Was this question useful?
👍 0 Helpful 👎 0 Not helpful
Yes 0% No 0%
0 responsesStudent Reviews
No published reviews yet.
