Any help with these 3 calc questions will be appreciated!
The link to the chart is below:
media. cheggcdn.com /media/a86/ a86f85b4-821e-4c06-863d-126b863efdae/ phpwYmomy
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 2/pi feet per second. Find the rate at which the volume is decreasing when the radius of Balloon B is 2 feet.
C. The cost to maintain inventory for the weather balloons is given by C(x)=21,000/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
2 answers
∆v ≈ dv/dt ∆t
so, ∆t = 0.5, making
∆v ≈ 4πr^2 ∆t = 4π*4*0.5 = 8π
If the graph is concave down, then the tangent line lies above the graph, meaning the approximation is too large.
B. using the chain rule,
dv/dt = 4πr^2 dr/dt
dv/dt = 4π*2^2(-2/π) = -32 ft^3/s
C. The marginal cost is dC/dx = -21000/x^2 + 2.4
So now just find C'(100)
1 answer