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

1. (a) \(k=0.125\)
2. (b) \(m=120e^{-0.125t}\)
3. (c) 5.55 hours

1. (a) \(k=0.04\)
2. (b) 4560

1. (a) \(y=-\tfrac13\ln\left(A-\tfrac32e^{2x}\right)\)
2. (b) \(y=\ln\left(\tfrac32e^{2x}-\tfrac12\right)\)

\(y=-\sqrt{11-2e^{-2x}}\)

1. (a) Shown: \(k=10\)
2. (b) \(r=\sqrt{20t+625}\)
3. (c) 48.8 hours

1. (a) \(v=20\left(1-e^{-0.45t}\right)\)
2. (b) 42.9 m

1. (a) \(\dfrac{dr}{dt}=-0.0857\)
2. (b) 22.5 hours

1. (a) \(\dfrac{dT}{dt}=-k(T-18),\ k>0\)
2. (b) \(T=18+67e^{-0.0584t}\)
3. (c) 29.5 minutes

1. (a) Shown
2. (b) \(m=125-100e^{-0.016t}\)
3. (c) 86.6 minutes
4. (d) 125 kg

1. (a) Shown: \(2\cos y+\sin x=c\)
2. (b) \(y=\pm0.723\)