# What was the temperature of the object?

1. Jan 12, 2015

### Math10

1. The problem statement, all variables and given/known data
An object is placed in a room where the temperature is 20 degrees Celsius. The temperature of the object drops by 5 degrees Celsius in 4 minutes and by 7 degrees Celsius in 8 minutes. What was the temperature of the object when it was initially placed in the room?

2. Relevant equations
Newton's law of cooling: T(t)=Ta+(To-Ta)e^(-kt)

3. The attempt at a solution
T(t)=Ta+(To-Ta)e^(-kt)
I know that I need to solve for To, which is the initial temperature but I don't know what to do.

2. Jan 12, 2015

### Bystander

Rewrite Newton in terms of delta T and see if that gives you any ideas.

3. Jan 12, 2015

### Staff: Mentor

4. Jan 12, 2015

### HallsofIvy

Staff Emeritus
When t= 4 min, T(4)= Ta+ (To- Ta)e^(-4k)= 15. When t= 8 min, T(8)= Ta+ (To- Ta)e^(-8k)= 13.
What do you get if you subtract e^(-8k)T(4)- e^(-4k)T(8)?

You are asked to find T(0)= To.

5. Jan 13, 2015

### Math10

I got it! Thanks everyone for the help!