A tumor is approximately modeled by the shape of a sphere, given by the following equation: 3 V = = r* (1) where V, is the volume of the spherical tumor and r, the radius. Data shows that, when the diameter of a spherical tumor is 16 mm then it is growing at a rate of 0.4 mm a day. How fast is the volume of the tumor changing at that time, mathematically this is symbolised by the derivative ? Solve the above problem through the following steps: (a) Apply the chain rule to equation 1 to find after writing r as r (t), because r is a function of time, t. Your answer will include r' (t) = 4[4] (b) Information of the size of this tumor is given in diameter measurement, convert this to radius measurement for r and r' (t) = [2] (c) Lastly, substitute the answers of (b) into the "answer equation" that you found in (a), to calculate 12)
A tumor is approximately modeled by the shape of a sphere, given by the following equation: 3 V = = r* (1) where V, is the volume of the spherical tumor and r, the radius. Data shows that, when the diameter of a spherical tumor is 16 mm then it is growing at a rate of 0.4 mm a day. How fast is the volume of the tumor changing at that time, mathematically this is symbolised by the derivative ? Solve the above problem through the following steps: (a) Apply the chain rule to equation 1 to find after writing r as r (t), because r is a function of time, t. Your answer will include r' (t) = 4[4] (b) Information of the size of this tumor is given in diameter measurement, convert this to radius measurement for r and r' (t) = [2] (c) Lastly, substitute the answers of (b) into the "answer equation" that you found in (a), to calculate 12)
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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![A tumor is approximately modeled by the shape of a sphere, given by the following equation:
3
V =
= r*
(1)
where V, is the volume of the spherical tumor and r, the radius. Data shows that, when the diameter
of a spherical tumor is 16 mm then it is growing at a rate of 0.4 mm a day. How fast is the volume of
the tumor changing at that time, mathematically this is symbolised by the derivative ?
Solve the above problem through the following steps:
(a) Apply the chain rule to equation 1 to find after writing r as r (t), because r is a function of
time, t. Your answer will include r' (t) = 4[4]
(b) Information of the size of this tumor is given in diameter measurement, convert this to radius
measurement for r and r' (t) = [2]
(c) Lastly, substitute the answers of (b) into the "answer equation" that you found in (a), to calculate
12)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F67d1892e-2dd2-40c5-b8d0-53e51bd6d89d%2Feb820957-0124-428a-9b4b-835dd2274c68%2Fxrw72k.jpeg&w=3840&q=75)
Transcribed Image Text:A tumor is approximately modeled by the shape of a sphere, given by the following equation:
3
V =
= r*
(1)
where V, is the volume of the spherical tumor and r, the radius. Data shows that, when the diameter
of a spherical tumor is 16 mm then it is growing at a rate of 0.4 mm a day. How fast is the volume of
the tumor changing at that time, mathematically this is symbolised by the derivative ?
Solve the above problem through the following steps:
(a) Apply the chain rule to equation 1 to find after writing r as r (t), because r is a function of
time, t. Your answer will include r' (t) = 4[4]
(b) Information of the size of this tumor is given in diameter measurement, convert this to radius
measurement for r and r' (t) = [2]
(c) Lastly, substitute the answers of (b) into the "answer equation" that you found in (a), to calculate
12)
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