Items left in a warehouse are given by I(d) = 250 − 15d. When will 100 items be left?
Answer and explanation
Correct answer: d = 10
This situation is represented by a linear decay function because the inventory decreases by the same amount, 15 items, for each increase of one day. To determine when the inventory is 100, substitute the target into the model: 250 − 15d = 100. Subtracting 100 from 250 gives 15d = 150. Dividing both sides by 15 yields d = 10. A substitution check gives I(10) = 250 − 15(10) = 250 − 150 = 100, confirming the answer. Hence option C is correct. The alternatives give different amounts: I(8) = 130, I(9) = 115, and I(15) = 25. Therefore none of them satisfies the stated target of 100 items.
Frequently asked questions
What is the correct answer to this question?
d = 10
Why is this the correct answer?
This situation is represented by a linear decay function because the inventory decreases by the same amount, 15 items, for each increase of one day. To determine when the inventory is 100, substitute the target into the model: 250 − 15d = 100. Subtracting 100 from 250 gives 15d = 150. Dividing both sides by 15 yields d = 10. A substitution check gives I(10) = 250 − 15(10) = 250 − 150 = 100, confirming the answer. Hence option C is correct. The alternatives give different amounts: I(8) = 130, I(9) = 115, and I(15) = 25. Therefore none of them satisfies the stated target of 100 items.
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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