A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by the function below. 1 3 P'(t) = (10t+10)(²+2t+2) ² Find the total profit in the first three years. (...) 5 The profit in the first three years is S ng (Round to the nearest dollar as needed.)
A small company of science writers found that its rate of profit (in thousands of dollars) after t years of operation is given by the function below. 1 3 P'(t) = (10t+10)(²+2t+2) ² Find the total profit in the first three years. (...) 5 The profit in the first three years is S ng (Round to the nearest dollar as needed.)
Calculus: Early Transcendentals
8th Edition
ISBN:9781285741550
Author:James Stewart
Publisher:James Stewart
Chapter1: Functions And Models
Section: Chapter Questions
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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![**Problem Statement:**
A small company of science writers found that its rate of profit (in thousands of dollars) after *t* years of operation is given by the function below.
\[ P'(t) = (10t + 10) \left( t^2 + 2t + 2 \right) ^{\frac{1}{3}} \]
**Task:**
Find the total profit in the first three years.
**Solution:**
To find the total profit in the first three years, we need to integrate the rate of profit function \( P'(t) \) from \( t = 0 \) to \( t = 3 \).
\[ P(3) = \int_{0}^{3} P'(t) \, dt \]
**Input Box:**
The profit in the first three years is $ [input box] (Round to the nearest dollar as needed.)
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Transcribed Image Text:**Problem Statement:**
A small company of science writers found that its rate of profit (in thousands of dollars) after *t* years of operation is given by the function below.
\[ P'(t) = (10t + 10) \left( t^2 + 2t + 2 \right) ^{\frac{1}{3}} \]
**Task:**
Find the total profit in the first three years.
**Solution:**
To find the total profit in the first three years, we need to integrate the rate of profit function \( P'(t) \) from \( t = 0 \) to \( t = 3 \).
\[ P(3) = \int_{0}^{3} P'(t) \, dt \]
**Input Box:**
The profit in the first three years is $ [input box] (Round to the nearest dollar as needed.)
**Buttons Available:**
- **Ask my instructor**
- **Clear all**
- **Show work**
- **Check answer**
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