Discussion about math, puzzles, games and fun.   Useful symbols: ÷ × ½ √ ∞ ≠ ≤ ≥ ≈ ⇒ ± ∈ Δ θ ∴ ∑ ∫ • π ƒ -¹ ² ³ °

You are not logged in.

## #1 2013-10-27 17:31:55

mrpace
Member

Offline

### Quick calculus question

dT/dt = -k(T-T1)

The question then states that this means that T(t)=T1+Ce^(-kt)

I don't see how they got that...can you help please?

## #2 2013-10-27 17:48:32

Agnishom
Real Member

Offline

### Re: Quick calculus question

You will get that if you integrate both sides

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #3 2013-10-27 17:54:31

mrpace
Member

Offline

### Re: Quick calculus question

#### Agnishom wrote:

You will get that if you integrate both sides

maybe you can show me?

## #4 2013-10-27 18:16:52

Agnishom
Real Member

Offline

### Re: Quick calculus question

Someone else might do it. I cannot

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'
'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'
'The whole person changes, why can't a habit?' -Alokananda

## #5 2013-10-27 19:56:44

bob bundy
Moderator

Offline

### Re: Quick calculus question

hi mrpace

Fisrtly, note that T and t represent different variables here.

One method for solving this is called "separation of variables".  You have to get all the T terms on one side and all the t terms on the other

Strictly speaking the dT/dt is not separable like this as it represents 0/0, but it works out ok if you quickly put in integration signs.

Now integrate each side.  The right hand side is easy as it is just integrate a constant with respect to t.  The left hand side is a natural log.

As D is just the constant of integration you can replace it with ln(C), another constant.

Bring the two log terms together using the rules for logs and then re-write the expression with e to get the required expression.

I've left a few steps for you.  Post back if you need more help.

Bob

You cannot teach a man anything;  you can only help him find it within himself..........Galileo Galilei