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

College Algebra (MindTap Course List)
12th Edition
ISBN:9781305652231
Author:R. David Gustafson, Jeff Hughes
Publisher:R. David Gustafson, Jeff Hughes
Chapter5: Exponential And Logarithmic Functions
Section5.5: Properties Of Logarithms
Problem 106E
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I need help with part b
rate of change, r' (t) for the radius of Balloon A over the time interval 0 <t < 10.
function r, of time t, where t is measured in minutes. The table below gives selected values of the
being inflated with hydrogen, the radius of the balloon, in feet, is modeled by a twice-differentiable
Weather Bots is a manufacturer of neoprene weather balloons. As the 350-gram spherical
t (minutes)
7
9.
10
4
r'(t)
(feet per minute)
3.7
2.6
1.3
0.9
0.4
0.25
** he radius of Balloon A is 5 feet whent = 4 minutes Estimate the radius of the balloon when
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 =
C. The cost to maintain inventory for the weather balloons is given by C(x) =
where x is the number of balloons in inventory. Find the marginal cost for adding the 101st
halloon to the inventory. Explain the meaning of this extra balloon in context to the scenario.
21,500
+ 2.4x,
Mcca) = Cc)
lel st
Ballon is acb
to the invertert
the maintances
Cost is 8.29dJat
21S00
when
+2.4
=.21500
10201
+ 2.4
= -2.11+2,4
= .20 dellars
(101)2 +2,4
© Jean Adanıs Flamingo MathT, LLC
Transcribed Image Text:rate of change, r' (t) for the radius of Balloon A over the time interval 0 <t < 10. function r, of time t, where t is measured in minutes. The table below gives selected values of the being inflated with hydrogen, the radius of the balloon, in feet, is modeled by a twice-differentiable Weather Bots is a manufacturer of neoprene weather balloons. As the 350-gram spherical t (minutes) 7 9. 10 4 r'(t) (feet per minute) 3.7 2.6 1.3 0.9 0.4 0.25 ** he radius of Balloon A is 5 feet whent = 4 minutes Estimate the radius of the balloon when 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 = C. The cost to maintain inventory for the weather balloons is given by C(x) = where x is the number of balloons in inventory. Find the marginal cost for adding the 101st halloon to the inventory. Explain the meaning of this extra balloon in context to the scenario. 21,500 + 2.4x, Mcca) = Cc) lel st Ballon is acb to the invertert the maintances Cost is 8.29dJat 21S00 when +2.4 =.21500 10201 + 2.4 = -2.11+2,4 = .20 dellars (101)2 +2,4 © Jean Adanıs Flamingo MathT, LLC
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