5) The manager of a Fast Tech store has found that the rate of sales (in hundreds of dollars per day) of the new iphone, t days after it has been on the market, is shown in the table below 5 15 Number of days = t Rate of sales (hundreds of dollars per day) 0 50 48 10 40 37 20 32 Compute a Riemann sum using the right and left endpoints (sums) to estimate the total sales of the new iphone during the first 20 days after it has been put on the market. Use the average of the left and right sums.
5) The manager of a Fast Tech store has found that the rate of sales (in hundreds of dollars per day) of the new iphone, t days after it has been on the market, is shown in the table below 5 15 Number of days = t Rate of sales (hundreds of dollars per day) 0 50 48 10 40 37 20 32 Compute a Riemann sum using the right and left endpoints (sums) to estimate the total sales of the new iphone during the first 20 days after it has been put on the market. Use the average of the left and right sums.
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
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Problem 1RCC: (a) What is a function? What are its domain and range? (b) What is the graph of a function? (c) How...
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Transcribed Image Text:**Estimation of Sales Using Riemann Sums**
The manager of a Fast Tech store has recorded the rate of sales for a new iPhone, measured in hundreds of dollars per day, over the first 20 days since its market release. This data is illustrated in the table below.
---
**Sales Data**
| Number of days \( t \) | Rate of sales (hundreds of dollars per day) |
|------------------------|--------------------------------------------|
| 0 | 50 |
| 5 | 48 |
| 10 | 40 |
| 15 | 37 |
| 20 | 32 |
---
**Objective:**
Compute a Riemann sum using both the right and left endpoints to estimate the total sales of the new iPhone during the first 20 days. Use the average of the left and right sums for a better approximation.
**Steps for Calculation:**
1. **Left Endpoint Riemann Sum:**
- Calculate the sum using the initial data points starting from \( t = 0 \).
2. **Right Endpoint Riemann Sum:**
- Calculate the sum using the data points starting from \( t = 5 \).
3. **Average of the Two Sums:**
- Combine the computed left and right sums by averaging them to get the estimated total sales.
This methodology provides a way to analyze and estimate the sales performance of a product using mathematical models, assisting in inventory and marketing strategies.
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