Question

Write a recursive equation for this situation. You started a Sweater company and made 1425 pre-orders. You expect to sell 5% more each week.

A. S_n = S_(n-1) + 0.05S_(n-1)
B. S_n = S_(n-1) + 0.05S_1
C. S_n = S_1 + 0.05S_1
D. S_n = S_1 + 0.05S_(n-1)

Answer 1

The recursive equation for this situation is S_n = S_(n-1) + 0.05S_(n-1). It represents the number of pre-orders in each week, considering a 5% increase from the previous week.

Step-by-step explanation:

The recursive equation for this situation can be represented as:

Sn = Sn-1 + 0.05Sn-1

Where:

• Sn represents the number of pre-orders in the nth week
• Sn-1 represents the number of pre-orders in the previous week

This recursive equation takes into account that each week, the number of pre-orders increases by 5% compared to the previous week.

For example, if you started with 1425 pre-orders in the first week, in the second week it would be:

S2 = S1 + 0.05S1

Substituting S1 with 1425, we get:

S2 = 1425 + 0.05*1425

Calculating this expression gives us the number of pre-orders in the second week.