please help with part C Weather Bots is a manufacturer of neoprene weather balloons. As the 350-gram spherical balloon isbeing inflated with hydrogen, the radius of the balloon, in feet, is modeled by a twice-differentiablefunction r, of time t, where t is measured in minutes. The table below gives selected values of therate of change, r'(t) for the radius of Balloon A over the time interval 0 < t < 10.t (minutes)2479.10r'(t)(feet per minute)3.72.61.30.90.40.25A. The radius of Balloon A is 5 feet whent = 4 minutes. Estimate the radius of the balloon whent = 4.5, using the tangent line approximation at t = 4. It is known that the graph of r is concavedown for the time 0 < t < 10. Is your approximation greater than or less than the true value?B. Balloon B has been removed from service and the radius of the balloon is decreasing at a rateof - feet per second. Find the rate at which the volume is decreasing when the radius ofBalloon B is 2 feet. Given: V = ar³%3D21,500С. Thcostmaintain inventory for the weather balloons is given by C(x)2.4x ,where x is the number of balloons in inventory. Find the marginal cost for adding the 101stballoon to the inventory. Explain the meaning of this extra balloon in context to the scenario.

Answered: Image /qna-images/answer/24e78bf7-784c-44f5-84e6-4111675fd06d.jpg

C. The cost to maintain inventory for the weather balloons is given by C(x) 21,500 %3D + 2.4x , where x is the number of balloons in inventory. Find the marginal cost for adding the 101st balloon to the inventory. Explain the meaning of this extra balloon in context to the scenario.

C. The cost to maintain inventory for the weather balloons is given by C(x) 21,500 %3D + 2.4x , where x is the number of balloons in inventory. Find the marginal cost for adding the 101st balloon to the inventory. Explain the meaning of this extra balloon in context to the scenario.

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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Question

please help with part C

Weather Bots is a manufacturer of neoprene weather balloons. As the 350-gram spherical balloon is
being inflated with hydrogen, the radius of the balloon, in feet, is modeled by a twice-differentiable
function r, of time t, where t is measured in minutes. The table below gives selected values of the
rate of change, r'(t) for the radius of Balloon A over the time interval 0 < t < 10.
t (minutes)
2
4
7
9.
10
r'(t)
(feet per minute)
3.7
2.6
1.3
0.9
0.4
0.25
A. The radius of Balloon A is 5 feet whent = 4 minutes. Estimate the radius of the balloon when
t = 4.5, using the tangent line approximation at t = 4. It is known that the graph of r is concave
down for the time 0 < t < 10. Is your approximation greater than or less than the true value?
B. Balloon B has been removed from service and the radius of the balloon is decreasing at a rate
of - feet per second. Find the rate at which the volume is decreasing when the radius of
Balloon B is 2 feet. Given: V = ar³
%3D
21,500
С. Th
cost
maintain inventory for the weather balloons is given by C(x)
2.4x ,
where x is the number of balloons in inventory. Find the marginal cost for adding the 101st
balloon to the inventory. Explain the meaning of this extra balloon in context to the scenario.

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