Question

as a function of the number of sessions attended
architecture class:
$5 initial fee
$13 per session
initial value for architecture class: 5
rate of change for architecture class: 13
complete the table for architecture.
number of sessions | 0 | 1 | 2 | 3 | 4
total cost for architecture($) | 5 | 18 | 31 | 44 | 57
drawing class:
number of sessions | 0 | 1 | 2 | 3 | 4
total cost ($) | 0 | 16 | 32 | 48 | 64
initial value for drawing class: 0
rate of change for drawing class: 16
when does the architecture class cost less? choose all that apply.
1 session 2 sessions 3 sessions 4 sessions

Explanation:

Step1: Compare 1 session costs

Architecture: $18, Drawing: $16. Architecture > Drawing? No, 18 > 16? Wait, no—wait, the question is when architecture costs less. Wait, no, wait: Architecture's 1 session cost is $18, Drawing's is $16. Wait, maybe I misread. Wait, no, let's check again. Wait, the architecture table: 0 sessions: $5, 1: $18, 2: $31, 3: $44, 4: $57. Drawing table: 0: $0, 1: $16, 2: $32, 3: $48, 4: $64. So for each session:

1 session: Architecture $18 vs Drawing $16 → Architecture is more? Wait, no, the question is "when does the architecture class cost less?" Wait, maybe I made a mistake. Wait, no—wait, 1 session: Architecture $18, Drawing $16 → Architecture is more. 2 sessions: Architecture $31, Drawing $32 → Architecture is less (31 < 32). 3 sessions: Architecture $44, Drawing $48 → 44 < 48. 4 sessions: Architecture $57, Drawing $64 → 57 < 64. Wait, but the options are 1,2,3,4 sessions. Wait, let's re-express:

• 1 session: Arch:18, Draw:16 → Arch > Draw (so Arch does NOT cost less)
• 2 sessions: Arch:31, Draw:32 → 31 < 32 → Arch costs less
• 3 sessions: Arch:44, Draw:48 → 44 < 48 → Arch costs less
• 4 sessions: Arch:57, Draw:64 → 57 < 64 → Arch costs less

Wait, but the first option is "1 session"—but Arch is $18, Draw $16, so Arch is more. So the correct ones are 2,3,4 sessions? Wait, but let's check again. Wait, maybe I messed up the initial problem. Wait, the question is "When does the architecture class cost less? Choose ALL that apply."

So:

• 1 session: Arch 18 vs Draw 16 → Arch is more (so no)
• 2 sessions: Arch 31 vs Draw 32 → 31 < 32 → yes
• 3 sessions: Arch 44 vs Draw 48 → 44 < 48 → yes
• 4 sessions: Arch 57 vs Draw 64 → 57 < 64 → yes

Wait, but the options are 1 session, 2 sessions, 3 sessions, 4 sessions. So the correct ones are 2 sessions, 3 sessions, 4 sessions? Wait, but let's check the numbers again. Architecture: 0:5, 1:5+13=18, 2:18+13=31, 3:31+13=44, 4:44+13=57. Drawing: 0:0, 1:16, 2:32 (162), 3:48 (163), 4:64 (16*4). So:

1 session: 18 vs 16 → Arch more

2 sessions: 31 vs 32 → Arch less (31 < 32)

3 sessions: 44 vs 48 → Arch less (44 < 48)

4 sessions: 57 vs 64 → Arch less (57 < 64)

So the correct options are 2 sessions, 3 sessions, 4 sessions. Wait, but the options are:

• 1 session

• 2 sessions

• 3 sessions

• 4 sessions

So we need to choose all that apply. So 2 sessions, 3 sessions, 4 sessions. Wait, but let's confirm again.

Step2: Verify 2 sessions

Arch:31, Draw:32 → 31 < 32 ✔️

Step3: Verify 3 sessions

Arch:44, Draw:48 → 44 < 48 ✔️

Step4: Verify 4 sessions

Arch:57, Draw:64 → 57 < 64 ✔️

Answer:

2 sessions, 3 sessions, 4 sessions (i.e., the options: 2 sessions, 3 sessions, 4 sessions)