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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.

Currently 350350 bales of hay are stored in a barn. Each day, a farmer stacks 3030 more bales of hay in the barn. Let H H be the number of bales of hay in the barn after t t days have passed. Which of the following best explains the relationship between t t and H H ?\newlineChoose 11 answer:\newline(A) The relationship is exponential because H H increases by 6060 as t t increases from t=0 t=0 to t=2 t=2 .\newline(B) The relationship is linear because H H decreases by 55 as t t increases from t=0 t=0 to t=1 t =1.\newline(C) The relationship is linear because H H increases by 3030 each time t t increases by 11 .\newline(D) The relationship is linear because H H always increases as t t increases.

Full solution

Q. Currently 350350 bales of hay are stored in a barn. Each day, a farmer stacks 3030 more bales of hay in the barn. Let H H be the number of bales of hay in the barn after t t days have passed. Which of the following best explains the relationship between t t and H H ?\newlineChoose 11 answer:\newline(A) The relationship is exponential because H H increases by 6060 as t t increases from t=0 t=0 to t=2 t=2 .\newline(B) The relationship is linear because H H decreases by 55 as t t increases from t=0 t=0 to t=1 t =1.\newline(C) The relationship is linear because H H increases by 3030 each time t t increases by 11 .\newline(D) The relationship is linear because H H always increases as t t increases.
  1. Understand Initial Condition: Understand the initial condition and the rate of change.\newlineThe problem states that there are initially 350350 bales of hay in the barn. Each day, the farmer adds 3030 more bales of hay. This suggests a starting value (initial condition) and a constant rate of change.
  2. Determine Relationship: Determine the relationship between tt and HH. Since the number of bales increases by a constant amount each day, the relationship between the number of days (tt) and the number of bales of hay (HH) is linear. This is because a linear relationship is defined by a constant rate of change.
  3. Check Answer Choices: Check the answer choices to find the one that correctly describes the relationship.\newline(A) Incorrect. The relationship is not exponential; it is linear because the increase in HH is by a constant amount, not by a percentage or factor.\newline(B) Incorrect. HH does not decrease; it increases by 3030 bales each day.\newline(C) Correct. This choice correctly states that the relationship is linear and that HH increases by 3030 each time tt increases by 11.\newline(D) Incorrect. While it is true that HH always increases as tt increases, this choice does not provide the specific rate of increase, which is necessary to fully describe the linear relationship.

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