Items remaining in a warehouse are modeled by I(d) = 200 − 12d. On what day will 80 items remain?
Answer and explanation
Correct answer: d = 10
The expression I(d) = 200 − 12d is a linear decay model. It starts at 200 items when d = 0 and decreases by 12 items for each additional day. To find when 80 items remain, set the model equal to the target value: 200 − 12d = 80. Subtracting 200 from both sides gives −12d = −120. Dividing by −12 gives d = 10. Substitution verifies the result: I(10) = 200 − 12(10) = 200 − 120 = 80. Therefore option C is correct. The other values produce 104, 92, and 56 items respectively, not 80.
Frequently asked questions
What is the correct answer to this question?
d = 10
Why is this the correct answer?
The expression I(d) = 200 − 12d is a linear decay model. It starts at 200 items when d = 0 and decreases by 12 items for each additional day. To find when 80 items remain, set the model equal to the target value: 200 − 12d = 80. Subtracting 200 from both sides gives −12d = −120. Dividing by −12 gives d = 10. Substitution verifies the result: I(10) = 200 − 12(10) = 200 − 120 = 80. Therefore option C is correct. The other values produce 104, 92, and 56 items respectively, not 80.
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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