I don't believe my answer is correct... can anyone help?

1.Newton's Law of Cooling. According to Newton's law of cooling, if an object at temperature T is immersed in a medium having the constant temperature M, then the rate of change of T is proportional to the difference of temperature MT. This gives the differential equation

dT/dt = k(M - T)

a.Solve the differential equation for T..

dT/dt = k(M - T)

dt[dT/dt = k(M - T)]

dT = k(M - T) dt

[dT = k(M - T) dt] 1/(M - T)

1/(M - T) dT = k dt

1/(M - T) dT = k dt

1/(M - T) dT = k dt

Ln |M - T| = kt

e^{Ln |M - T|} = e^kt

|M - T| = e^kt

|M| - |T| = e^kt

- |T| = e^kt - |M|

T = M - e^kt + C where M - T 0 or M T and M and T are positive real numbers (hence, the absolute value).

b.A thermometer reading 100F is placed in a medium having a constant temperature of 70F. After 6 min, the thermometer reads 80F. What is the reading after 20 min?

T = 100; M = 70; t = 0; k = 0;

T(0) = 100

100 = 70 - e^k(0) + C

100 = 70 - e⁰ + C

100 = 70 - 1 + C

100 = 69 + C

31 = C

M = 70; t = 6; k = 20; C = 31

T(6) = ?, what's T?

|T| = |M| - e^kt + C

|T| = (|70| - e^(20)(6)) + 31

|T| = 70 - e¹²⁰ + 31

|T| = 101 - e¹²⁰

T = .