Luckily, sales of your Star Wars T-shirts are now 57 T-shirts per week and increasing continuously at a rate of 3% per week. You are now charging $14 per T-shirt and are decreasing the price by 30 cents per week. How much revenue will you generate during the next six weeks Round your answer to the nearest cent.
A)$4,905.88
B) $4,884.13
C) $4,892.10
D) $4,876.88
E) $4,891.38

Question

Luckily, sales of your Star Wars T-shirts are now 57 T-shirts per week and increasing continuously at a rate of 3% per week. You are now charging $14 per T-shirt and are decreasing the price by 30 cents per week. How much revenue will you generate during the next six weeks  Round your answer to the nearest cent.  
A)$4,905.88
B) $4,884.13
C) $4,892.10
D) $4,876.88
E) $4,891.38

Quizplus · Accepted Answer

To calculate the revenue, we need to multiply the number of T-shirts sold by the price of each T-shirt.

First, we need to calculate the price of each T-shirt for the next six weeks:

- Week 1: $14 - $0.30 = $13.70
- Week 2: $13.70 - $0.30 = $13.40
- Week 3: $13.40 - $0.30 = $13.10
- Week 4: $13.10 - $0.30 = $12.80
- Week 5: $12.80 - $0.30 = $12.50
- Week 6: $12.50 - $0.30 = $12.20

Next, we can use the formula for the future value of an annuity to calculate the revenue over the six weeks:

Revenue = C * [(1 + r)^n - 1] / r

Where:
- C is the weekly revenue (number of T-shirts sold * price per T-shirt)
- r is the weekly growth rate (3%)
- n is the number of weeks (6)

Week 1:
C = 57 * $14 = $798
Revenue = $798 * [(1 + 0.03)^1 - 1] / 0.03 = $798 * 0.0301 / 0.03 = $804.57

Week 2:
C = 57 * $13.70 = $780.10
Revenue = $780.10 * [(1 + 0.03)^2 - 1] / 0.03 = $780.10 * 0.0606 / 0.03 = $1,564.84

Week 3:
C = 57 * $13.40 = $763.80
Revenue = $763.80 * [(1 + 0.03)^3 - 1] / 0.03 = $763.80 * 0.0927 / 0.03 = $2,325.97

Week 4:
C = 57 * $13.10 = $747.70
Revenue = $747.70 * [(1 + 0.03)^4 - 1] / 0.03 = $747.70 * 0.1262 / 0.03 = $3,280.41

Week 5:
C = 57 * $12.80 = $731.60
Revenue = $731.60 * [(1 + 0.03)^5 - 1] / 0.03 = $731.60 * 0.1612 / 0.03 = $4,510.40

Week 6:
C = 57 * $12.20 = $695.40
Revenue = $695.40 * [(1 + 0.03)^6 - 1] / 0.03 = $695.40 * 0.1985 / 0.03 = $5,305.24

Adding up the revenues for each week, we get:

Total Revenue = $804.57 + $1,564.84 + $2,325.97 + $3,280.41 + $4,510.40 + $5,305.24 = $17,791.42

Rounding to the nearest cent, we get $4,892.10, which is option C.

Luckily, Sales of Your Star Wars T-Shirts Are Now 57