Aiden is reading a book for History class. He records the number of pages, p, he reads as a function of the time, t, in hours, as shown. At what average rate of change, in pages per hours, does Aiden read his book from t=.5 to t=3? Enter your answer as a decimal rounded to the nearest tenth. ✓ T √ Submit
Aiden is reading a book for History class. He records the number of pages, p, he reads as a function of the time, t, in hours, as shown. At what average rate of change, in pages per hours, does Aiden read his book from t=.5 to t=3? Enter your answer as a decimal rounded to the nearest tenth. ✓ T √ Submit
Trigonometry (11th Edition)
11th Edition
ISBN:9780134217437
Author:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Publisher:Margaret L. Lial, John Hornsby, David I. Schneider, Callie Daniels
Chapter1: Trigonometric Functions
Section: Chapter Questions
Problem 1RE:
1. Give the measures of the complement and the supplement of an angle measuring 35°.
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Question
![Aiden is reading a book for History class. He records the number of pages, \( p \), he reads as a function of the time, \( t \), in hours, as shown.
**Question:**
At what average rate of change, in pages per hour, does Aiden read his book from \( t = 0.5 \) to \( t = 3 \)? Enter your answer as a decimal rounded to the nearest tenth.
**Table Data:**
\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
t & 0 & 0.5 & 1 & 1.5 & 2 & 2.5 & 3 & 3.5 \\
\hline
p(t) & 0 & 22 & 41 & 65 & 80 & 103 & 115 & 132 \\
\hline
\end{array}
\]
**Explanation:**
The table lists values of \( t \) in hours, and corresponding values of \( p(t) \), the number of pages read. The question asks for the average rate of change in pages per hour from \( t = 0.5 \) to \( t = 3 \).
To calculate the average rate of change, use the formula:
\[
\text{Average rate of change} = \frac{p(t_2) - p(t_1)}{t_2 - t_1}
\]
Substitute \( t_1 = 0.5 \), \( t_2 = 3 \), \( p(t_1) = 22 \), and \( p(t_2) = 115 \) into the formula:
\[
\text{Average rate of change} = \frac{115 - 22}{3 - 0.5} = \frac{93}{2.5} = 37.2
\]
So, the average rate of change is 37.2 pages per hour.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F1c3f0c16-4bc2-4005-8b34-f5a8ba23d8d8%2F9991a53e-055e-403d-8bdc-bf4e0dfdc6cb%2Fzcejha_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Aiden is reading a book for History class. He records the number of pages, \( p \), he reads as a function of the time, \( t \), in hours, as shown.
**Question:**
At what average rate of change, in pages per hour, does Aiden read his book from \( t = 0.5 \) to \( t = 3 \)? Enter your answer as a decimal rounded to the nearest tenth.
**Table Data:**
\[
\begin{array}{|c|c|c|c|c|c|c|c|}
\hline
t & 0 & 0.5 & 1 & 1.5 & 2 & 2.5 & 3 & 3.5 \\
\hline
p(t) & 0 & 22 & 41 & 65 & 80 & 103 & 115 & 132 \\
\hline
\end{array}
\]
**Explanation:**
The table lists values of \( t \) in hours, and corresponding values of \( p(t) \), the number of pages read. The question asks for the average rate of change in pages per hour from \( t = 0.5 \) to \( t = 3 \).
To calculate the average rate of change, use the formula:
\[
\text{Average rate of change} = \frac{p(t_2) - p(t_1)}{t_2 - t_1}
\]
Substitute \( t_1 = 0.5 \), \( t_2 = 3 \), \( p(t_1) = 22 \), and \( p(t_2) = 115 \) into the formula:
\[
\text{Average rate of change} = \frac{115 - 22}{3 - 0.5} = \frac{93}{2.5} = 37.2
\]
So, the average rate of change is 37.2 pages per hour.
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