A pulse laser operates by storing charge on a capacitor and releasing it suddenly when the laser is fired. The data in the table describe the charge Q remaining on the capacitor (measured in coulombs) at time t (measured in seconds after the laser is fired). Use the data to draw the graph of this function and estimate the slope of the tangent line at the point where t = 0.04. (Note: The slope of the tangent line represents the electric current flowing from the capacitor to the laser (measured in amperes).) tQ 0.00 10 0.02 8.187 0.04 6.702 0.06 5.487 0.08 4.492 0.10 3.678 Solution In the following figure we plot the data and use it to sketch a curve that approximates the graph of the function. MpR Q (coulombs) 10 8 6 4 2 0.02 0.04 0.06 0.08 0.10 Given the points P(0.04, 6.702) and R(0.00, 10) on the graph, we find that the slope of the secant line PR, rounded to two decimal places, is as follows. 10-( 0.00 -0.04 The following table shows the results of similar calculations for the slopes of other secant lines. (0.00, 10) (0.02, 8.187) (0.06 5 487) PR t (seconds) -82.45 -74.25 60 75
A pulse laser operates by storing charge on a capacitor and releasing it suddenly when the laser is fired. The data in the table describe the charge Q remaining on the capacitor (measured in coulombs) at time t (measured in seconds after the laser is fired). Use the data to draw the graph of this function and estimate the slope of the tangent line at the point where t = 0.04. (Note: The slope of the tangent line represents the electric current flowing from the capacitor to the laser (measured in amperes).) tQ 0.00 10 0.02 8.187 0.04 6.702 0.06 5.487 0.08 4.492 0.10 3.678 Solution In the following figure we plot the data and use it to sketch a curve that approximates the graph of the function. MpR Q (coulombs) 10 8 6 4 2 0.02 0.04 0.06 0.08 0.10 Given the points P(0.04, 6.702) and R(0.00, 10) on the graph, we find that the slope of the secant line PR, rounded to two decimal places, is as follows. 10-( 0.00 -0.04 The following table shows the results of similar calculations for the slopes of other secant lines. (0.00, 10) (0.02, 8.187) (0.06 5 487) PR t (seconds) -82.45 -74.25 60 75
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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Transcribed Image Text:A pulse laser operates by storing charge on a capacitor and releasing it suddenly when the laser is fired. The data in the table
describe the charge Q remaining on the capacitor (measured in coulombs) at time t (measured in seconds after the laser is fired).
Use the data to draw the graph of this function and estimate the slope of the tangent line at the point where t = 0.04. (Note: The
slope of the tangent line represents the electric current flowing from the capacitor to the laser (measured in amperes).)
0.00 10
0.02 8.187
mpg"
0.04 6.702
0.06 5.487
0.08 4.492
0.10 3.678
Solution
In the following figure we plot the data and use it to sketch a curve that approximates the graph of the function.
Q(coulombs)
10%
8
6
4
2
Q
Given the points P(0.04, 6.702) and R(0.00, 10) on the graph, we find that the slope of the secant line PR, rounded to two
decimal places, is as follows.
10 -(
0.00 0.04
The following table shows the results of similar calculations for the slopes of other secant lines.
(0.00, 10)
(0.02, 8.187)
(0.06, 5.487)
R
(0.08, 4.492)
(0.10, 3.678)
0.02 0.04 0.06 0.08 0.10
Q (coulombs)
10
8
6
4
2
mpR
From this table we would expect the slope of the tangent line at t = 0.04 to lie somewhere between -74.25 and -60.75. In fact,
the average of the slopes of the two closest secant lines is as follows.
(-74.25-60.75) = [
A
-82.45
So, by this method, we estimate the slope of the tangent line, rounded to the nearest integer, to be about
Another method is to draw an approximation to the tangent line at P and measure the sides of the triangle ABC, as in the figure.
below.
B
-74.25
-60.75
-55.25
-50.40
t (seconds)
P
t (seconds)
0.02 0.04 0.06 0.08 0.10
=-67.05.
This gives an estimate of the slope of the tangent line as
5.361-8.043
|AB|
|BC|
0.06 -0.02
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