Detailed derivation:
dA/dt = 6 - 0.02A
dA/dt = -0.02 (A - 300)
Rearranging terms.
dA / (A - 300) = -0.02 dt
Integrate both sides.
ln(A - 300) = -0.02t + C
Isolate A.
A - 300 = Ce^(-0.02t)
A = 300 + Ce^(-0.02t)
Apply initial condition to determine C.
50 = 300 + Ce^(-0.02 × 10)
50 = 300 + Ce^(-0.2)
-250 = Ce^(-0.2)
C = -250e^(0.2)
A = 300 - 250e^(0.2)e^(-0.02t)
A = 300 - 250e^(0.2 - 0.02t)
I trust this will assist you.
Both a and b must be positive whole numbers.
