question number two

Question

Which function satisfies the equation below? (c is an arbitrary constant.)

dB/dt= (-0.05)B

1. B = c(-0.025)t²
2. B = c(-0.025)B²   
3. B = c(-0.05)t
4. B = ce^(-0.05)t
5. B = ce^t

Answer 1

dB/dt = - 0.05B

dB/B = - 0.05dt

∫ dB/B =- ∫0.05dt

ln |B| = - 0.05t +k

|B| = e^{( -0.05t +k)}

|B| = e^k e^-0.05

|B| = λ e^-0.05t

B = ± λ e^-0.05t

B = c e^-0.05t