#25- The revenue R (in millions of dollars) for P.F. Chang's China Bistro from 2001 through 2009 can be modeled by R=295.1+147.665fInt, |≤+≤9, where it is the year, with t=1 corresponding to 2001. Find the total revenue from 2001 through 2009. (fnint it)
#25- The revenue R (in millions of dollars) for P.F. Chang's China Bistro from 2001 through 2009 can be modeled by R=295.1+147.665fInt, |≤+≤9, where it is the year, with t=1 corresponding to 2001. Find the total revenue from 2001 through 2009. (fnint it)
Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
Publisher:Erwin Kreyszig
Chapter2: Second-order Linear Odes
Section: Chapter Questions
Problem 1RQ
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![### Problem #25: Revenue Model for P.F. Chang's China Bistro
The revenue \( R \) (in millions of dollars) for P.F. Chang's China Bistro from 2001 through 2009 can be modeled by:
\[ R = 295.1 + 147.66\sqrt{t} \]
where \( 1 \leq t \leq 9 \), and \( t \) is the year with \( t = 1 \) corresponding to 2001.
**Task:**
Find the total revenue from 2001 through 2009.
To solve this, you need to integrate the revenue function over the given time period. The integration will provide the accumulated revenue over the years specified.
### Steps for Solution:
1. **Setup the Integral**: Integrate the given revenue function with respect to \( t \) over the interval from \( t = 1 \) to \( t = 9 \).
\[
\int_{1}^{9} (295.1 + 147.66\sqrt{t}) \, dt
\]
2. **Compute the Integral**: Perform the integration and evaluate the definite integral within the specified bounds.
By following these steps, you can find the total revenue for P.F. Chang's China Bistro from 2001 through 2009.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F818e2187-d92f-4dcd-a2a4-628a60c1b962%2F1c35180d-9ad0-40b3-8b44-e84d5a37ba0e%2Fj5cdakw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Problem #25: Revenue Model for P.F. Chang's China Bistro
The revenue \( R \) (in millions of dollars) for P.F. Chang's China Bistro from 2001 through 2009 can be modeled by:
\[ R = 295.1 + 147.66\sqrt{t} \]
where \( 1 \leq t \leq 9 \), and \( t \) is the year with \( t = 1 \) corresponding to 2001.
**Task:**
Find the total revenue from 2001 through 2009.
To solve this, you need to integrate the revenue function over the given time period. The integration will provide the accumulated revenue over the years specified.
### Steps for Solution:
1. **Setup the Integral**: Integrate the given revenue function with respect to \( t \) over the interval from \( t = 1 \) to \( t = 9 \).
\[
\int_{1}^{9} (295.1 + 147.66\sqrt{t}) \, dt
\]
2. **Compute the Integral**: Perform the integration and evaluate the definite integral within the specified bounds.
By following these steps, you can find the total revenue for P.F. Chang's China Bistro from 2001 through 2009.
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