Annual sales (in millions of units) of a certain model of phone are expected to grow in accordance with the function f(t) = 0.3t² +0.14t + 5.1 where t is measured in years, with t = 0 corresponding to the year 2018. Which of the following integrals would be used to determine the average number of phones sold over the 4-year period from 2019 to 2023? (0.163 (0.1³ +0.072 +5.1t) dt 5 S (0.3t² + 0.14t+5.1) dt 4- (0.3+² (0.3+2 +0.14t+5.1) dt (0.3t² +0.14t + 5.1) dt 2023 2019
Annual sales (in millions of units) of a certain model of phone are expected to grow in accordance with the function f(t) = 0.3t² +0.14t + 5.1 where t is measured in years, with t = 0 corresponding to the year 2018. Which of the following integrals would be used to determine the average number of phones sold over the 4-year period from 2019 to 2023? (0.163 (0.1³ +0.072 +5.1t) dt 5 S (0.3t² + 0.14t+5.1) dt 4- (0.3+² (0.3+2 +0.14t+5.1) dt (0.3t² +0.14t + 5.1) dt 2023 2019
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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![### Calculating Average Sales over a Given Period
#### Problem Statement
Annual sales (in millions of units) of a certain model of phone are expected to grow in accordance with the function:
\[ f(t) = 0.3t^2 + 0.14t + 5.1 \]
where \( t \) is measured in years, with \( t = 0 \) corresponding to the year 2018.
**Question:** Which of the following integrals would be used to determine the **average** number of phones sold over the 4-year period from 2019 to 2023?
#### Given Options:
1. \[
\frac{1}{4} \int_{0}^{4} \left( 0.1t^3 + 0.07t^2 + 5.1t \right) dt
\]
2. \[
\frac{1}{4} \int_{1}^{5} \left( 0.3t^2 + 0.14t + 5.1 \right) dt
\]
3. \[
\frac{1}{4} \int_{0}^{4} \left( 0.3t^2 + 0.14t + 5.1 \right) dt
\]
4. \[
\frac{1}{4} \int_{2019}^{2023} \left( 0.3t^2 + 0.14t + 5.1 \right) dt
\]
#### Explanation:
To determine the average number of phones sold over a 4-year period from 2019 to 2023, we must calculate the integral of the sales function over that time period and then divide by the length of the period (which is 4 years).
Let's break down the options:
- **Option 1:** This integral \(\frac{1}{4} \int_{0}^{4} \left( 0.1t^3 + 0.07t^2 + 5.1t \right) dt\) is incorrect because it does not match the given function \( f(t) \).
- **Option 2:** This integral \(\frac{1}{4} \int_{1}^{5} \left( 0.3t^2 + 0.14t + 5.1 \right) dt\](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Ffbc3f4f4-d793-4827-8e3d-2f51535d2e99%2F57340939-d116-41d8-ab29-f9d520d44e98%2F9a2uxz_processed.jpeg&w=3840&q=75)
Transcribed Image Text:### Calculating Average Sales over a Given Period
#### Problem Statement
Annual sales (in millions of units) of a certain model of phone are expected to grow in accordance with the function:
\[ f(t) = 0.3t^2 + 0.14t + 5.1 \]
where \( t \) is measured in years, with \( t = 0 \) corresponding to the year 2018.
**Question:** Which of the following integrals would be used to determine the **average** number of phones sold over the 4-year period from 2019 to 2023?
#### Given Options:
1. \[
\frac{1}{4} \int_{0}^{4} \left( 0.1t^3 + 0.07t^2 + 5.1t \right) dt
\]
2. \[
\frac{1}{4} \int_{1}^{5} \left( 0.3t^2 + 0.14t + 5.1 \right) dt
\]
3. \[
\frac{1}{4} \int_{0}^{4} \left( 0.3t^2 + 0.14t + 5.1 \right) dt
\]
4. \[
\frac{1}{4} \int_{2019}^{2023} \left( 0.3t^2 + 0.14t + 5.1 \right) dt
\]
#### Explanation:
To determine the average number of phones sold over a 4-year period from 2019 to 2023, we must calculate the integral of the sales function over that time period and then divide by the length of the period (which is 4 years).
Let's break down the options:
- **Option 1:** This integral \(\frac{1}{4} \int_{0}^{4} \left( 0.1t^3 + 0.07t^2 + 5.1t \right) dt\) is incorrect because it does not match the given function \( f(t) \).
- **Option 2:** This integral \(\frac{1}{4} \int_{1}^{5} \left( 0.3t^2 + 0.14t + 5.1 \right) dt\
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