Separable equations in context: growth, decay and harder forms Problem set A Answers

1. (a) \(k=0.12\)
2. (b) \(m=60e^{-0.12t}\)
3. (c) 5.78 days

1. (a) \(k=0.07\)
2. (b) 1220

1. (a) \(y=-\ln\left(A-\tfrac13e^{3x}\right)\)
2. (b) \(y=\tfrac14\ln\left(20e^{x}-19\right)\)

\(y=-\sqrt{10-6e^{-x}}\)

1. (a) Shown: \(k=20\)
2. (b) \(h=\sqrt{40t+1600}\)
3. (c) 50.0 min

1. (a) \(v=40\left(1-e^{-0.35t}\right)\)
2. (b) 45.7 m

1. (a) \(\dfrac{dr}{dt}=-0.0592\)
2. (b) 24.0 minutes

1. (a) \(\dfrac{dT}{dt}=-k(T-22),\ k>0\)
2. (b) \(T=22+128e^{-0.0826t}\)
3. (c) 23.8 minutes

1. (a) Shown
2. (b) \(m=30-20e^{-0.02t}\)
3. (c) 34.7 minutes
4. (d) 30 kg

1. (a) Shown: \(\cos y+2\sin x=c\)
2. (b) \(y=\pm1.05\)