The dollar valuation V(t) of Batcoin as a function of time t, measured in days, is governedby the differential equation:dVdt-0.04V² + 80V(a) For what initial valuations would Batcoin remain priced at the same level?(b) Sketch a direction field describing this situation. You may assume that the Batcoinvaluation never dips below zero.(c) Would Batcoin ever become essentially worthless? Justify your answer.(d) If you purchased a single Batcoin at its market price of $2500 today, approximately howmuch would your investment be worth six months from now? Use graphical analysis andexplain your answer.=

Given the differential equation , where V(t) is the dollar valuation of Batcoin as a function of t…

Answered: The dollar valuation V(t) of Batcoin as…

Advanced Engineering Mathematics

10th Edition

ISBN:9780470458365

Author:Erwin Kreyszig

Publisher:Erwin Kreyszig

Chapter2: Second-order Linear Odes

Section: Chapter Questions

Problem 1RQ

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At time t = 0, a bacterial culture weighs 2 grams. Three hours later, the culture weighs 5 grams. The maximum weight of the culture is 20 grams. (a) Write a logistic equation that models the weight of the bacterial culture. (Round your coefficients to four decimal places.) 20 y = dy dt = 1 +9e 8 g (c) When will the culture's weight reach 16 grams? (Round your answer to two decimal places.) 9.79 hr (d) Write a logistic differential equation that models the growth rate of the culture's weight. Then repeat part (b) using Euler's Method with a step size of h = 1. (Round your answer to the nearest whole number.) y(5) = 6 -0.3662t = 1.37 0.366y| 1 (1-20) (b) Find the culture's weight after 5 hours. (Round your answer to the nearest whole number.) X g (e) At what time is the culture's weight increasing most rapidly? (Round your answer to two decimal places.) hr
The population, P, of kangaroos in a reservation is modelled by the logistic dP equation = dt 2P (5- reservation. - P 10 000 ) where t is measured in days. It is estimated that initially the population of the kangaroos is 15% of the carrying capacity of the (i) What is the initial population of the kangaroos? (ii) What is the population of the kangaroos when the rate of increase is a maximum?
A child inflates a balloon, admires it for a while and then lets the air out at a constant rate. If V(t) gives the volume of the balloon at time t, then the figure shows V'(t) as a function of t. At what time does the child do each of the following? y'(t) 1 -2 3 (a) begin to inflate the balloon? t = (b) finish inflating the balloon? t = (c) begin to let the air out? it = 1 6 0-2 3 3 (d) What would the graph of V'(t) look like if the child had alternated between pinching and releasing the open end of the balloon, instead of letting the air out at a constant rate? '(t) V'(t) 6 9 6 9 12 15 v'(t) 9 12 15 18 12 t 18 t nna: 15 18 1 -2 3 6 6 9 v'(t) 9 12 15 18 12 18 t t
X Three holes are made (one at the south pole, and one at the equator, for leaking, one at the north pole for air intake) to enable the same draining constant k for the leaking holes. The draining process follows the IVP A(h)dh -k√h Z The inside of a container is an ellipsoid (as shown) 2 2 (²) ² + (²)² + (²³)² = b 1 h = dt h(t = 0) = ho y introduced by Torricelli in 1643. In the DE, A (h) is the cross-section area at the height (from the leaking point) h. Derive the formula for the time needed to empty a fully filled tank. Note: Both leaking holes are at work while draining the upper half tank and, naturally, only one hole leaks while draining the lower half.

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