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1 answer:
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Answer:
(a) -dA/dt = kA², A₀ = 10
(b) A =10/(1+ kt)
(c) t > 60 h
Step-by-step explanation:
(a) Find the IVP
A differential equation with an initial condition y₀ = f(x₀) is called an initial value problem.
The rate of decrease of A is proportional to A², and A₀ = 10, so the IVP is
-dA/dt = kA², A₀ = 10
(b) Solve the IVP
Apply the initial condition: A₀ = 10 (when t = 0)
(c) Find the time when A(t) < 1
(i) Find the value of k (A₁₀ = 4)
(ii) Find t when A < 1
The figure below shows the graph of A vs t.
