EXAMPLE 2 The flash unit on a camera operates by storing charge on a capacitor and releasing it suddenly when the flash is set off. The data in the table describe the charge Q remaining on the capacitor (measured in microcoulombs) at time t (measured in seconds after the flash goes off). 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 flash bulb (measured in microamperes).] SOLUTION In the figure we plot the data and use it to sketch a curve that approximates the graph of the function. Given the points P(0.04, 67.03) and R(0.00, 100.00) on the graph, we find that the slope of the secant line PR is 100.00 - mPR = 0.00 - 0.04 The table at the left shows the results of similar calculations for the slopes of other secant lines. From this table we would expect the slope of the tangent line at t = 0.04 to lie somewhere between -741.50 and -607.00. In fact, the average of the slopes of the two closest secant lines is 0.5(-741.50 - 607.00) = So, by this method, we estimate the slope of the tangent line to be (rounded to the nearest integer). Another method is to draw an approximation to the tangent line at Pand measure the sides of the triangle ABC, as in the figure. This gives an estimate of the slope of the tangent line as JAB| BCI 80.4 - 53.6 0.06 - 0.02 = -670.
EXAMPLE 2 The flash unit on a camera operates by storing charge on a capacitor and releasing it suddenly when the flash is set off. The data in the table describe the charge Q remaining on the capacitor (measured in microcoulombs) at time t (measured in seconds after the flash goes off). 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 flash bulb (measured in microamperes).] SOLUTION In the figure we plot the data and use it to sketch a curve that approximates the graph of the function. Given the points P(0.04, 67.03) and R(0.00, 100.00) on the graph, we find that the slope of the secant line PR is 100.00 - mPR = 0.00 - 0.04 The table at the left shows the results of similar calculations for the slopes of other secant lines. From this table we would expect the slope of the tangent line at t = 0.04 to lie somewhere between -741.50 and -607.00. In fact, the average of the slopes of the two closest secant lines is 0.5(-741.50 - 607.00) = So, by this method, we estimate the slope of the tangent line to be (rounded to the nearest integer). Another method is to draw an approximation to the tangent line at Pand measure the sides of the triangle ABC, as in the figure. This gives an estimate of the slope of the tangent line as JAB| BCI 80.4 - 53.6 0.06 - 0.02 = -670.
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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Rate of Change
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Slope
The change in the vertical distances is known as the rise and the change in the horizontal distances is known as the run. So, the rise divided by run is nothing but a slope value. It is calculated with simple algebraic equations as:
Question
![EXAMPLE 2
The flash unit on a camera operates by storing charge on a capacitor and releasing it suddenly when the flash is set off. The data in the table
describe the charge Q remaining on the capacitor (measured in microcoulombs) at time t (measured in seconds after the flash goes off). 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 flash bulb (measured in microamperes).]
SOLUTION
In the figure we plot the data and use it to sketch a curve that approximates the graph of the function.
Given the points P(0.04, 67.03) and R(0.00, 100.00) on the graph, we find that the slope of the secant line PR is
100.00 -
MPR
0.00 0.04
-
The table at the left shows the results of similar calculations for the slopes of other secant lines. From this table we would expect the slope of the tangent line at t
= 0.04 to lie somewhere between -741.50 and -607.00. In fact, the average of the slopes of the two closest secant lines is
0.5(-741.50 - 607.00)
%3D
So, by this method, we estimate the slope of the tangent line to be
(rounded to the nearest integer).
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. This gives an estimate of the
slope of the tangent line as
AB
IBC|
80.4 53.6
= -670.
0.06 0.02](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F59458a28-92bf-4235-8093-85cfbdfd45ce%2F47bc924a-96af-4298-a979-afc49f381498%2Fr9ahaw_processed.jpeg&w=3840&q=75)
Transcribed Image Text:EXAMPLE 2
The flash unit on a camera operates by storing charge on a capacitor and releasing it suddenly when the flash is set off. The data in the table
describe the charge Q remaining on the capacitor (measured in microcoulombs) at time t (measured in seconds after the flash goes off). 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 flash bulb (measured in microamperes).]
SOLUTION
In the figure we plot the data and use it to sketch a curve that approximates the graph of the function.
Given the points P(0.04, 67.03) and R(0.00, 100.00) on the graph, we find that the slope of the secant line PR is
100.00 -
MPR
0.00 0.04
-
The table at the left shows the results of similar calculations for the slopes of other secant lines. From this table we would expect the slope of the tangent line at t
= 0.04 to lie somewhere between -741.50 and -607.00. In fact, the average of the slopes of the two closest secant lines is
0.5(-741.50 - 607.00)
%3D
So, by this method, we estimate the slope of the tangent line to be
(rounded to the nearest integer).
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. This gives an estimate of the
slope of the tangent line as
AB
IBC|
80.4 53.6
= -670.
0.06 0.02
Transcribed Image Text:0.00 100.00
0.02 81.86
0.04 67.03
0.06 54.89
0.08 44.91
0.10 36.77
21 (microooulombs)
100
90
70
60
50
B.
0.02
0,04
0.06
0.08
0.1
I (seconds)
mPR
(0.00, 100.00)| -824.25
(0.02,81.86)
-741.50
(0.06, 54.89)
-607.00
(0.08, 44.91)
-553.00
(0.10, 36.77)
504,33
R.
8822 8
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