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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.

College Algebra (MindTap Course List)
College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter2: Functions And Graphs
Section2.6: Proportion And Variation
Problem 18E
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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.
Transcribed Image Text: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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