a) The radius of Balloon A is 5 feet when t = 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:  c) The cost for Raven Industries to maintain inventory for chloroprene balloons is given by the function , 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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