Question

1. A bucket is filled from a hose that has a constant flow rate. Is the amount of water in the bucket best described by a linear or exponential function of time during the filling process? Explain.

A. Since the amount added per unit time is constant, the amount of water in the bucket increases by a constant amount for equal time intervals. This is an exponential function.
B. Since the amount added per unit time is constant, the amount of water in the bucket is multiplied by a constant factor for equal time intervals. This is an linear function.
C. Since the amount added per unit time is constant, the amount of water in the bucket increases by a constant amount for equal time intervals. This is a linear function.
D. Since the amount added per unit time is constant, the amount of water in the bucket is multiplied by a constant factor for equal time intervals. This is an exponential function.
2. A bond is purchased for $1,000 that pays 6 percent of the purchase price annually. Is the amount earned described by a linear or exponential function?
A. A bond is purchased for $1,000 that pays 6 percent of the purchase price annually. Is the amount earned described by a linear or exponential function?
B. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is a linear function.
C. The interest paid each year is constant, so the amount earned is multiplied by a constant factor for equal time intervals. This is an exponential function.
D. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is an exponential function.
3. A savings account has an initial balance of $1,000 and earns 3 percent interest compounded monthly. Is the balance of the account described by a linear or exponential function?
A. The interest paid each month is a factor of the current balance, so the balance increases by a constant value for equal time intervals. This is an exponential function.
B. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is an exponential function.
C. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is a linear function.
D. The interest paid each month is a factor of the current balance, so the balance increases by a constant value for equal time intervals. This is a linear function.

Answer 1

Answer: Your welcome!

Explanation:

1. Answer: D. Since the amount added per unit time is constant, the amount of water in the bucket is multiplied by a constant factor for equal time intervals. This is an exponential function. As time increases, the amount of water in the bucket will increase exponentially (each successive unit of time will add a multiple of the original amount).

2. A. The amount earned is described by a linear function. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is a linear function.

3. Answer: B. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is an exponential function.

An exponential function is one in which the value of a variable increases or decreases by a constant factor for each equal time interval. In this case, the balance of the savings account increases by a fixed amount of interest each month, which is calculated from the current balance. This amount is multiplied by the current balance, resulting in an exponential function.

Answer 2

C. Since the amount added per unit time is constant, the amount of water in the bucket increases by a constant amount for equal time intervals. This is a linear function.

B. The interest paid each year is constant, so the amount earned increases by a constant amount for equal time intervals. This is a linear function.

B. The interest paid each month is a factor of the current balance, so the balance is multiplied by a constant factor for equal time intervals. This is an exponential function.

Explanation: