# Semi Logs assignment

• May 23rd 2011, 07:27 PM
FearTheHump
Semi Logs assignment
Hi, first of all - sorry if this is in the wrong forum, I'm from Australia and have no idea what the difference between pre-calculus and calculus is, or if this is even a calculus related question at all.

That said, I am having some trouble wording this maths assignment (which is due tomorrow -_-). I know exactly what to do and it's not hard at all (in terms of the maths), but I don't know how to express this as proof that my answer is correct.

Basically, the assignment required us to get temperature data from 2 cups of coffee over 7 minutes - one black, and one white with 30ml of milk. We then needed to determine the probably temperature after 12 minutes.

We've been told to make use of Newton's Law of Cooling:
T - T1 = (T0 - T1)e^(-kt), and semi logs to find k.

All well and good, I went and found the answer, blah blah blah. But the main marks in the assignment come from justifying that answer and showing how I got to it.

Now, this is where I might start to sound like an idiot. I understand that semi log graphs are used to show exponential data with a linear function, right? So you take the data, graph the natural log of the whole thing and use the gradient and y-int to find the original function in the form of y=Ae^(kt), etc.

But...how can I show that this is what I've done?

So far I've written this, but I'm not sure if it's concise enough:

Quote:

According to Newton’s Law of Cooling, the rate of cooling can be expressed as an exponential function: T - T1 = (T0 - T1)e^(-kt)

In order to find the value of k, a semi-log graph (Y = mx + c) can be formed, if we let:
• Y = ln(T – T1)
• m = k
• c = ln(T0 – T1)

∴ ln(T-T1) = kx + ln(T0 – T1)
How can I then go and say "So yeah, now we plug the data into a calculator, pull some numbers out of thin air and put them into this other function over here and wala we have a function"??

I'm so confused =(
• May 23rd 2011, 07:41 PM
eulcer
Some advice just for now, name your variables, and make it clear what they stand for, that may look a bit better. You could also show the middle step between the law of cooling and "semi-logs" where you determine than you may take the log of both sides of your equality as the domain is unrestricted in this case considering the fact all values inside the log will be positive since it is in fact cooling. You said you can explain the use of the linear model, yes?
• May 23rd 2011, 07:42 PM
mr fantastic
Quote:

Originally Posted by FearTheHump
Hi, first of all - sorry if this is in the wrong forum, I'm from Australia and have no idea what the difference between pre-calculus and calculus is, or if this is even a calculus related question at all.

That said, I am having some trouble wording this maths assignment (which is due tomorrow -_-). I know exactly what to do and it's not hard at all (in terms of the maths), but I don't know how to express this as proof that my answer is correct.

Basically, the assignment required us to get temperature data from 2 cups of coffee over 7 minutes - one black, and one white with 30ml of milk. We then needed to determine the probably temperature after 12 minutes.

We've been told to make use of Newton's Law of Cooling:
T - T1 = (T0 - T1)e^(-kt), and semi logs to find k.

All well and good, I went and found the answer, blah blah blah. But the main marks in the assignment come from justifying that answer and showing how I got to it.

Now, this is where I might start to sound like an idiot. I understand that semi log graphs are used to show exponential data with a linear function, right? So you take the data, graph the natural log of the whole thing and use the gradient and y-int to find the original function in the form of y=Ae^(kt), etc.

But...how can I show that this is what I've done?

So far I've written this, but I'm not sure if it's concise enough:

How can I then go and say "So yeah, now we plug the data into a calculator, pull some numbers out of thin air and put them into this other function over here and wala we have a function"??

I'm so confused =(