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The dollar valuation V ( t ) of Batcoin as a function of time t , measured in days, is governed by the differential equation:

The dollar valuation V (t) of Batcoin as a function of time t, measured in days, is governed
by the differential equation:
dV/dt =0.04V^2+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 Batcoin
valuation 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 how
much would your investment be worth six months from now? Use graphical analysis and
explain your answer.

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