5. A swimming pool is being filled with a hose. The functionf (t) = 12t gives the amount of water in the pool (in gallons) after t minutes. The function g(h) = 60h gives the number of minutes in h hours. Calculate (f • g)(5) and explain what the result means about the swimming pool. Include units in your answer.
5. A swimming pool is being filled with a hose. The functionf (t) = 12t gives the amount of water in the pool (in gallons) after t minutes. The function g(h) = 60h gives the number of minutes in h hours. Calculate (f • g)(5) and explain what the result means about the swimming pool. Include units in your answer.
Algebra and Trigonometry (6th Edition)
6th Edition
ISBN:9780134463216
Author:Robert F. Blitzer
Publisher:Robert F. Blitzer
ChapterP: Prerequisites: Fundamental Concepts Of Algebra
Section: Chapter Questions
Problem 1MCCP: In Exercises 1-25, simplify the given expression or perform the indicated operation (and simplify,...
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**Problem 5:**
A swimming pool is being filled with a hose. The function \( f(t) = 12t \) gives the amount of water in the pool (in gallons) after \( t \) minutes. The function \( g(h) = 60h \) gives the number of minutes in \( h \) hours. Calculate \( (f \circ g)(5) \) and explain what the result means about the swimming pool. Include units in your answer.
**Solution Explanation:**
To solve this problem, we need to use function composition, represented by \( (f \circ g)(5) \). This involves taking the output of \( g(h) \) and using it as the input for \( f(t) \).
1. **Calculate \( g(5) \):**
\[
g(h) = 60h
\]
\[
g(5) = 60 \times 5 = 300
\]
This means there are 300 minutes in 5 hours.
2. **Calculate \( f(g(5)) \) or \( f(300) \):**
\[
f(t) = 12t
\]
\[
f(300) = 12 \times 300 = 3600
\]
This means that after 300 minutes, the pool will have 3600 gallons of water.
**Conclusion:**
By calculating \( (f \circ g)(5) \), we determine that in 5 hours, the swimming pool will be filled with 3600 gallons of water. The use of function composition allows us to effectively combine the two functions to understand the relationship between time and the amount of water filled.
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Transcribed Image Text:Certainly! Here's a detailed transcription for an educational website:
---
**Problem 5:**
A swimming pool is being filled with a hose. The function \( f(t) = 12t \) gives the amount of water in the pool (in gallons) after \( t \) minutes. The function \( g(h) = 60h \) gives the number of minutes in \( h \) hours. Calculate \( (f \circ g)(5) \) and explain what the result means about the swimming pool. Include units in your answer.
**Solution Explanation:**
To solve this problem, we need to use function composition, represented by \( (f \circ g)(5) \). This involves taking the output of \( g(h) \) and using it as the input for \( f(t) \).
1. **Calculate \( g(5) \):**
\[
g(h) = 60h
\]
\[
g(5) = 60 \times 5 = 300
\]
This means there are 300 minutes in 5 hours.
2. **Calculate \( f(g(5)) \) or \( f(300) \):**
\[
f(t) = 12t
\]
\[
f(300) = 12 \times 300 = 3600
\]
This means that after 300 minutes, the pool will have 3600 gallons of water.
**Conclusion:**
By calculating \( (f \circ g)(5) \), we determine that in 5 hours, the swimming pool will be filled with 3600 gallons of water. The use of function composition allows us to effectively combine the two functions to understand the relationship between time and the amount of water filled.
---
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