Question

the student center also offers an architecture class. the description shows the total cost of a class, y, as a function of the number of sessions attended, x. 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, blank, blank, blank. 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.

Explanation:

Step1: Identify the cost formula

The total cost \( y \) for architecture class is \( y = 5 + 13x \), where \( x \) is the number of sessions.

Step2: Calculate for \( x = 2 \)

Substitute \( x = 2 \) into the formula: \( y = 5 + 13\times2 = 5 + 26 = 31 \)? Wait, no, wait. Wait, the initial value is 5 (when \( x = 0 \)), and rate of change is 13 per session. Wait, when \( x = 1 \), cost is \( 5 + 13\times1 = 18 \), which matches the table. So for \( x = 2 \): \( 18 + 13 = 31 \)? Wait, no, wait, maybe I made a mistake. Wait, the formula is \( y = 5 + 13x \). So for \( x = 2 \), \( y = 5 + 13*2 = 5 + 26 = 31 \). For \( x = 3 \): \( 5 + 13*3 = 5 + 39 = 44 \). For \( x = 4 \): \( 5 + 13*4 = 5 + 52 = 57 \). Wait, but let's check the pattern. From \( x = 0 \) to \( x = 1 \), it's 5 to 18, which is +13. So each session adds 13. So after \( x = 1 \) (18), \( x = 2 \) is \( 18 + 13 = 31 \), \( x = 3 \) is \( 31 + 13 = 44 \), \( x = 4 \) is \( 44 + 13 = 57 \).

Wait, but maybe I misread the initial fee. The problem says $5 initial fee, $13 per session. So the function is \( y = 5 + 13x \), where \( x \) is the number of sessions. So:

• \( x = 0 \): \( 5 + 13*0 = 5 \) (matches)
• \( x = 1 \): \( 5 + 13*1 = 18 \) (matches)
• \( x = 2 \): \( 5 + 13*2 = 5 + 26 = 31 \)
• \( x = 3 \): \( 5 + 13*3 = 5 + 39 = 44 \)
• \( x = 4 \): \( 5 + 13*4 = 5 + 52 = 57 \)

So the table for architecture should be:

Number of Sessions: 0, 1, 2, 3, 4

Total Cost: 5, 18, 31, 44, 57

Wait, but let's confirm the rate of change. The rate of change is 13, so each time \( x \) increases by 1, \( y \) increases by 13. So from \( x = 1 \) (18) to \( x = 2 \), add 13: 18 + 13 = 31. Then \( x = 3 \): 31 + 13 = 44. \( x = 4 \): 44 + 13 = 57.

Answer:

For the architecture class table:

• Number of Sessions = 2: Total Cost = 31
• Number of Sessions = 3: Total Cost = 44
• Number of Sessions = 4: Total Cost = 57

So the completed table cells (from left to right, the empty ones) are 31, 44, 57.