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 Algebra Pre-Algebra and Basic Algebra Math Forum

 September 5th, 2007, 09:36 PM #1 Newbie   Joined: Sep 2007 Posts: 1 Thanks: 0 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. September 6th, 2007, 07:29 AM #2 Global Moderator   Joined: Nov 2006 From: UTC -5 Posts: 16,046 Thanks: 938 Math Focus: Number theory, computational mathematics, combinatorics, FOM, symbolic logic, TCS, algorithms 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. Tags h or w, logaritm Thread Tools Show Printable Version Email this Page Display Modes Linear Mode Switch to Hybrid Mode Switch to Threaded Mode Similar Threads Thread Thread Starter Forum Replies Last Post b2kguga Calculus 1 July 23rd, 2011 02:41 PM Riazy Calculus 1 February 16th, 2011 10:37 PM geyikrali Real Analysis 1 February 23rd, 2008 01:14 AM ananda Calculus 0 December 31st, 1969 04:00 PM

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