If D(t) = 88 - 4t, by how much will D(t) decrease when t increases by 1?
Answer and explanation
Correct answer: 4
The governing concept is the constant rate of change in a linear expression. In D(t) = 88 - 4t, the coefficient of t is -4, so increasing t by one changes the value by -4. Directly, D(t+1) = 88 - 4(t+1) = 88 - 4t - 4 = D(t) - 4. Hence the function value becomes 4 smaller, and the positive amount of decrease is 4, making option C correct. Option B is the signed change, not the amount by which the value decreases. Option A is the initial constant term, and option D would be the value only for a particular input such as t = 1, not the change.
Frequently asked questions
What is the correct answer to this question?
4
Why is this the correct answer?
The governing concept is the constant rate of change in a linear expression. In D(t) = 88 - 4t, the coefficient of t is -4, so increasing t by one changes the value by -4. Directly, D(t+1) = 88 - 4(t+1) = 88 - 4t - 4 = D(t) - 4. Hence the function value becomes 4 smaller, and the positive amount of decrease is 4, making option C correct. Option B is the signed change, not the amount by which the value decreases. Option A is the initial constant term, and option D would be the value only for a particular input such as t = 1, not the change.
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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