7. After tennis practice, Wong places tennis balls into canisters. He can use up to 10 canisters, and he places exactly 3 tennis balls into each canister. The number of tennis balls placed into canisters is a function of the number of canisters.

Question

Which statements are true regarding the domain and range of this function? Select all that apply.
A.
The domain of the function is all real numbers from 0 to 10.

B.
The domain of the function is all whole numbers from 0 to 10.

C.
The domain of the function is all whole numbers from 0 to 30.

D.
The range of the function is all multiples of 3 from 0 to 30.

E.
The range of the function is all whole numbers from 0 to 30.

8. A local farm deposits 1.5 ft3 of fertilizer into a storage container at a garden store each week. After 5 weeks the container has 15 ft3 of fertilizer.

If it takes 14 more weeks for the storage container to be filled, what is the capacity of the storage container?

A.
21 ft3

B.
36 ft3

C.
28.5 ft3

D.
43.5 ft3

Answer 1

Question 7

The function's domain is determined by the number of canisters Wong can use, which is from 0 to a maximum of 10 canisters. Therefore:

• A. The domain of the function is all real numbers from 0 to 10. (False) This statement includes all real numbers, which isn't accurate since the number of canisters must be whole numbers.

• B. The domain of the function is all whole numbers from 0 to 10. (True) This accurately describes the canister count, as Wong can use from 0 to 10 (inclusive) whole canisters.

• C. The domain of the function is all whole numbers from 0 to 30. (False) This is not true since the maximum number of canisters is only 10.

For the range, the function calculates the number of tennis balls based on the canisters. Since there are 3 tennis balls in each canister:

• If Wong uses 0 canisters: 0 tennis balls
• If he uses 1 canister: 3 tennis balls
• If he uses 2 canisters: 6 tennis balls
• ...
• If he uses 10 canisters: 30 tennis balls

Thus, the possible number of tennis balls is 0, 3, 6, 9, 12, 15, 18, 21, 24, 27, and 30. All of these results are multiples of 3.

• D. The range of the function is all multiples of 3 from 0 to 30. (True) This accurately describes the range based on how many canisters are used.

• E. The range of the function is all whole numbers from 0 to 30. (False) While the outputs are whole numbers, not every whole number between 0 and 30 can be achieved; only the multiples of 3 can be.

True Statements: B and D.

Question 8

Wong deposits 1.5 ft³ of fertilizer weekly. After 5 weeks, he has:

\[ 1.5 , \text{ft}^3 \times 5 = 7.5 , \text{ft}^3 \]

He mentions that after 5 weeks the container has 15 ft³, meaning 15 ft³ - 7.5 ft³ = 7.5 ft³ is still to be deposited.

Now, if it takes 14 more weeks to fill the storage container with the same rate, we can calculate the total amount deposited in those 14 weeks:

\[ 1.5 , \text{ft}^3 \times 14 = 21 , \text{ft}^3 \]

Adding this to the amount already deposited (15 ft³):

\[ 15 , \text{ft}^3 + 21 , \text{ft}^3 = 36 , \text{ft}^3 \]

Thus, the capacity of the storage container is B. 36 ft³.