Currently 350 bales of hay are stored in a barn. Each day, a farmer stacks 30 more bales of hay in the barn. Let H be the number of bales of hay in the barn after t days have passed. Which of the following best explains the relationship between t and H ? Choose 1 answer: (A) The relationship is exponential because H increases by 60 as t increases from t=0 to t=2. (B) The relationship is linear because H decreases by 5 as t increases from t=0 to t=1. (C) The relationship is linear because H increases by 30 each time t increases by 1 . (D) The relationship is linear because H always increases as t increases.

Question

Currently 350 bales of hay are stored in a barn. Each day, a farmer stacks 30 more bales of hay in the barn. Let  H be the number of bales of hay in the barn after  t days have passed. Which of the following best explains the relationship between  t and  H ? Choose 1 answer: (A) The relationship is exponential because  H increases by 60 as  t increases from  t=0 to  t=2. (B) The relationship is linear because  H decreases by 5 as  t increases from  t=0 to  t=1. (C) The relationship is linear because  H increases by 30 each time  t increases by 1 . (D) The relationship is linear because  H always increases as  t increases.

Bytelearn · Accepted Answer

Understand Initial Condition: Understand the initial condition and the rate of change. The problem states that there are initially 350 bales of hay in the barn. Each day, the farmer adds 30 more bales of hay. This suggests a starting value (initial condition) and a constant rate of change.Determine Relationship: Determine the relationship between t and H. Since the number of bales increases by a constant amount each day, the relationship between the number of days (t) and the number of bales of hay (H) is linear. This is because a linear relationship is defined by a constant rate of change.Check Answer Choices: Check the answer choices to find the one that correctly describes the relationship. (A) Incorrect. The relationship is not exponential; it is linear because the increase in H is by a constant amount, not by a percentage or factor. (B) Incorrect. H does not decrease; it increases by 30 bales each day. (C) Correct. This choice correctly states that the relationship is linear and that H increases by 30 each time t increases by 1. (D) Incorrect. While it is true that H always increases as t increases, this choice does not provide the specific rate of increase, which is necessary to fully describe the linear relationship.

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