help with DE problem: Newton's law of cooling

At 1:00 PM, a thermometer reading 70 degrees F is taken outside where the temperature is -10 degrees F (ten below zero). At 1:02PM, the reading is 26 degrees. At 1:05PM the thermometer is taken back indoors, where the air is at 70 degrees F. What is the temperature reading at 1:09PM?

u is the temperature reading

u_o is the medium

and by integrating

my solutions in solving the problem:

"At 1:00 PM, a thermometer reading 70 degrees F is taken outside where the temperature is -10 degrees F (ten below zero)":

at t = 0 , u = 70

and u_o = 10

C = 80

Now we already know the constant

"At 1:02PM, the reading is 26 degrees":

at t = 2; u = 26

k = 0.39925

my problem is that i dont understand when it is put indoors

"At 1:05PM the thermometer is taken back indoors, where the air is at 70 degrees F":

the constant of proportionality is the same

....and i dont understand the problem

the answer to this problem is 56 degrees Farenheit