Modeling with periodic functions: Cyclical exponential decay. A spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 2 seconds the amplitude has decreased to 3 cm. Also, the spring oscillates 20 times each second. Assuming that the amplitude is decreasing exponentially, below is a model for the distance, D the end of the spring is below equilibrium, in terms of seconds, t: D(t) 17(0.42008)* . cos(407rt) . [Note: Here we define t as the number of seconds elapsed. Also, locations below the resting position have negative values for D.] After t = 5 seconds, how far from equilibrium is the end of the spring? If your answer is a decimal, please round to no more than 3 decimal places. cm *Notes: This foreshadows our upcoming topic of exponential functions. For an example of an exponential function (and how it's applied), check out this video [+]. To see where this equation came from, check out this video 2 [+].
Modeling with periodic functions: Cyclical exponential decay. A spring is attached to the ceiling and pulled 17 cm down from equilibrium and released. After 2 seconds the amplitude has decreased to 3 cm. Also, the spring oscillates 20 times each second. Assuming that the amplitude is decreasing exponentially, below is a model for the distance, D the end of the spring is below equilibrium, in terms of seconds, t: D(t) 17(0.42008)* . cos(407rt) . [Note: Here we define t as the number of seconds elapsed. Also, locations below the resting position have negative values for D.] After t = 5 seconds, how far from equilibrium is the end of the spring? If your answer is a decimal, please round to no more than 3 decimal places. cm *Notes: This foreshadows our upcoming topic of exponential functions. For an example of an exponential function (and how it's applied), check out this video [+]. To see where this equation came from, check out this video 2 [+].
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter5: Inverse, Exponential, And Logarithmic Functions
Section5.3: The Natural Exponential Function
Problem 27E
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![Modeling with periodic functions: Cyclical exponential decay. A spring is attached to the ceiling and pulled
17 cm down from equilibrium and released. After 2 seconds the amplitude has decreased to 3 cm. Also, the
spring oscillates 20 times each second. Assuming that the amplitude is decreasing exponentially, below is a
model for the distance, D the end of the spring is below equilibrium, in terms of seconds, t:
D(t) = 17(0.42008)* . cos(407rt) .
%3D
• C
[Note: Here we define t as the number of seconds elapsed. Also, locations below the resting position have
negative values for D.]
After t
If your answer is a decimal, please round to no more than 3 decimal places.
5 seconds, how far from equilibrium is the end of the spring?
cm
*Notes: This foreshadows our upcoming topic of exponential functions. For an example of an exponential
function (and how it's applied), check out this video 2 [+]. To see where this equation came from, check out
this video [+].](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F99694efa-53d4-40ed-8e15-9efc0175f356%2F44931fd6-a463-4e5a-a54e-e25d2fc49c73%2F4x4373m_processed.png&w=3840&q=75)
Transcribed Image Text:Modeling with periodic functions: Cyclical exponential decay. A spring is attached to the ceiling and pulled
17 cm down from equilibrium and released. After 2 seconds the amplitude has decreased to 3 cm. Also, the
spring oscillates 20 times each second. Assuming that the amplitude is decreasing exponentially, below is a
model for the distance, D the end of the spring is below equilibrium, in terms of seconds, t:
D(t) = 17(0.42008)* . cos(407rt) .
%3D
• C
[Note: Here we define t as the number of seconds elapsed. Also, locations below the resting position have
negative values for D.]
After t
If your answer is a decimal, please round to no more than 3 decimal places.
5 seconds, how far from equilibrium is the end of the spring?
cm
*Notes: This foreshadows our upcoming topic of exponential functions. For an example of an exponential
function (and how it's applied), check out this video 2 [+]. To see where this equation came from, check out
this video [+].
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