Revenue expontential calculus problem?
Help me please??
Sales of your current text, "Little House on the Prairie" are dropping. To increase sales, you have clearly decided to reduce the proce of your book, currently priced at $28, by $1 per week. Your book will really sell if you do that! You will sell 7550 copies this week alone. However, sales will, according to your sources, continue to decline at a rate of 7% per week. How much revenue will you earn over the next 5 weeks?
I believe this is a HINT for part of the setup... 7555e^(-.07....
Comments
As a discrete system with weekly adjustments:
week units .... price . revenue
0 ...... 7550 ... $28 ... $211400.00
1 ...... 7022 ... $27 ... $189580.50
2 ...... 6530 ... $26 ... $169779.87
3 ...... 6073 ... $25 ... $151822.38
4 ...... 5648 ... $24 ... $135547.02
∑ revenue = $858129.78
As a continuous system (revenue = price/unit x units sold):
r = 7550 ∫ (28 - t) (0.93)^t dt [0,5] = $812,093.69
Answer: see above