capacitor and releasing it suddenly when th- table describe the charge Q remaining on th microcoulombs) at time t (measured in seco the data to draw the graph of this function a tangent line at the point where t = 0.04. [M represents the electric current flowing from (measured in microamperes).]
capacitor and releasing it suddenly when th- table describe the charge Q remaining on th microcoulombs) at time t (measured in seco the data to draw the graph of this function a tangent line at the point where t = 0.04. [M represents the electric current flowing from (measured in microamperes).]
Big Ideas Math A Bridge To Success Algebra 1: Student Edition 2015
1st Edition
ISBN:9781680331141
Author:HOUGHTON MIFFLIN HARCOURT
Publisher:HOUGHTON MIFFLIN HARCOURT
Chapter8: Graphing Quadratic Functions
Section: Chapter Questions
Problem 30CR
Related questions
Question
![t e
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
0.00 100.00
table describe the charge Q remaining on the capacitor (measured in
0.02
81.89
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
0.04 67.04
tangent line at the point where t = 0.04. [Note: The slope of the tangent line
0.06 54.85
represents the electric current flowing from the capacitor to the flash bulb
0.08 44.93
(measured in microamperes).]
0.10 36.78
SOLUTION In the figure we plot the data and use it to sketch a curve that
ef (microooulombs)
approximates the graph of the function.
100
90
Given the points P(0.04, 67.04) and R(0.00, 100.00) on the graph, we find
80
that the slope of the secant line PR is
70
100.00 -
60
mpR =
0.00 – 0.04
50
B
Tcaconda) 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
0.02
0.04
0.06
0,08
0.1
mPR
line at t = 0.04 to lie somewhere between -742.50 and -609.50. In fact,
the average of the slopes of the two closest secant lines is
(0.00, 100.00) -824.00
0.5(-742.50 - 609.50) =
(0.02, 81.89)
-742.50
So, by this method, we estimate the slope of the tangent line to be
(0.06, 54.85)
-609.50
(rounded to the nearest integer).
(0.08, 44.93)
-552.75
(0.10, 36.78)
-504.33
Another method is to draw an approximation to the tangent line at P and
Video Example )
measure the sides of the triangle ABC, as in the figure. This gives an estimate
of the slope of the tangent line as
- JAB|
|BC|
80.4 - 53.6
= -670.
0.06 - 0.02](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2Fe82ebd42-ef68-41dc-8504-bf49f851fb6f%2Fd535a772-1cb3-4070-acdd-fca5a33df6ef%2Fwztk82_processed.jpeg&w=3840&q=75)
Transcribed Image Text:t e
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
0.00 100.00
table describe the charge Q remaining on the capacitor (measured in
0.02
81.89
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
0.04 67.04
tangent line at the point where t = 0.04. [Note: The slope of the tangent line
0.06 54.85
represents the electric current flowing from the capacitor to the flash bulb
0.08 44.93
(measured in microamperes).]
0.10 36.78
SOLUTION In the figure we plot the data and use it to sketch a curve that
ef (microooulombs)
approximates the graph of the function.
100
90
Given the points P(0.04, 67.04) and R(0.00, 100.00) on the graph, we find
80
that the slope of the secant line PR is
70
100.00 -
60
mpR =
0.00 – 0.04
50
B
Tcaconda) 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
0.02
0.04
0.06
0,08
0.1
mPR
line at t = 0.04 to lie somewhere between -742.50 and -609.50. In fact,
the average of the slopes of the two closest secant lines is
(0.00, 100.00) -824.00
0.5(-742.50 - 609.50) =
(0.02, 81.89)
-742.50
So, by this method, we estimate the slope of the tangent line to be
(0.06, 54.85)
-609.50
(rounded to the nearest integer).
(0.08, 44.93)
-552.75
(0.10, 36.78)
-504.33
Another method is to draw an approximation to the tangent line at P and
Video Example )
measure the sides of the triangle ABC, as in the figure. This gives an estimate
of the slope of the tangent line as
- JAB|
|BC|
80.4 - 53.6
= -670.
0.06 - 0.02
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 4 steps
Recommended textbooks for you
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Big Ideas Math A Bridge To Success Algebra 1: Stu…
Algebra
ISBN:
9781680331141
Author:
HOUGHTON MIFFLIN HARCOURT
Publisher:
Houghton Mifflin Harcourt
Algebra & Trigonometry with Analytic Geometry
Algebra
ISBN:
9781133382119
Author:
Swokowski
Publisher:
Cengage
Glencoe Algebra 1, Student Edition, 9780079039897…
Algebra
ISBN:
9780079039897
Author:
Carter
Publisher:
McGraw Hill