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September 5th, 2007, 09:36 PM   #1
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Logaritm H/W help

Hi all, I'm having a hard time figuring out how to do the last part of my homework, I would be grateful if someone could explain to me how to do this.

A cup of tea is cooling in the shade. T degrees Celsius, a spreadsheet was used to plot log e ( T ) against time, t, in minutes.
The spreadsheet calculated the line of best fit to have an equation expressed as Log e (T) = -0.045t + 4.4543

e is ~2.71 on the calculator.

1) Show that in exponential form this is equivalently written as T = e ^ (-0.045t + 4.4543).
I'm aware that using the Log law you can write that out in 1 step, but not sure how to prove it. Because going from
Log e (T) = -0.045t + 4.4543 ----> T = e ^ (-0.045t + 4.4543)
is done in 1 step.

2) Hence write the expression in the form T=Ae ^ -0.045t
Show that A=86 to the nearest correct integer.
Do i just substitute 86 in to A ?

3)The rule for T can also be written in the form T = 86 * 2 ^ -kt
a) If T = 86 * 2 ^ -kt =
86e ^ -0.045t
Find the value of K to 3 decimals
I actually have NO IDEA how to do this one ?!

b) Hence write the time taken for the Excess temperature (The initial temperature which is 86) to be halved and show that
K = 1/H
Let H be the Time.

If anyone could help me out that would be great, I'm going to need to learn this for my up-coming test in a week. Thanks everyone.
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September 6th, 2007, 07:29 AM   #2
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Re: Logaritm H/W help

1. Take the exponential of both sides. Then simplify the exponential of the logarithm of a number to the number itself, since these are inverses.

2. You're supposed to show that A is about 86 in this particular equation. You do this by taking exp(-0.045t + 4.4543), which is exp(-0.045t) * exp(4.4543). Simplify the second factor and you should get what you seek.

3. Just like #2, simplify the other equation by taking exp(-0.045t) = exp(-0.045)^t.
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