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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Equations and Inequations
Equations and inequalities describe the relationship between two mathematical expressions.
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A linear function can just be a constant, or it can be the constant multiplied with the variable like x or y. If the variables are of the form, x2, x1/2 or y2 it is not linear. The exponent over the variables should always be 1.
Question
P’(33)=$_____per year
![Title: Analyzing the Price Trend of Crude Oil (1980-2013)
The price per barrel of crude oil over the period 1980-2013, in constant 2014 dollars, can be approximated by the equation:
\[ P(t) = 0.27t^2 - 8.6t + 93 \]
where \( t \) is time in years since the start of 1980. The interval for \( t \) is \( 0 \le t \le 33 \).
To determine the rate at which the price changes over time (\( P'(t) \)), we find the derivative of \( P(t) \):
\[ P'(t) = 0.54t - 8.6 \]
Next, we need to evaluate \( P'(33) \):
\[ P'(33) = 0.54(33) - 8.6 \]
\[ P'(33) = 17.82 - 8.6 \]
\[ P'(33) = 9.22 \]
Thus, \( P'(33) = 9.22 \) dollars per year.
### Graphs and Diagrams Explanation:
There are no graphs or diagrams included in the image provided.
### Interpreting the Result:
The second result, \( P'(33) = 9.22 \), indicates that in the year 2013, the price of crude oil was increasing at a rate of $9.22 per year.
The price of a barrel of crude oil was increasing at a rate of $9.22 per year in 2013.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F577fc8a5-9a20-4139-b44d-30124c6f9476%2F32a1c008-423c-4d0c-abe2-e362b48cfd9b%2F04waax_processed.jpeg&w=3840&q=75)
Transcribed Image Text:Title: Analyzing the Price Trend of Crude Oil (1980-2013)
The price per barrel of crude oil over the period 1980-2013, in constant 2014 dollars, can be approximated by the equation:
\[ P(t) = 0.27t^2 - 8.6t + 93 \]
where \( t \) is time in years since the start of 1980. The interval for \( t \) is \( 0 \le t \le 33 \).
To determine the rate at which the price changes over time (\( P'(t) \)), we find the derivative of \( P(t) \):
\[ P'(t) = 0.54t - 8.6 \]
Next, we need to evaluate \( P'(33) \):
\[ P'(33) = 0.54(33) - 8.6 \]
\[ P'(33) = 17.82 - 8.6 \]
\[ P'(33) = 9.22 \]
Thus, \( P'(33) = 9.22 \) dollars per year.
### Graphs and Diagrams Explanation:
There are no graphs or diagrams included in the image provided.
### Interpreting the Result:
The second result, \( P'(33) = 9.22 \), indicates that in the year 2013, the price of crude oil was increasing at a rate of $9.22 per year.
The price of a barrel of crude oil was increasing at a rate of $9.22 per year in 2013.
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