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Question
Radioactivity Decay Let Q represent a mass of carbon 14(14^C)(in grams), whose half life is 5730 years. The quantity of carbon 14 present after t years is
Q= 10(1/2)^t/5730
(a) Determine the initial quantity (when t=0).
(b) Determine the quantity present after 2000 years
(c) sketch the graph of this function over the interval t=0 to t=10,000.

Answer
(a) If we want the quantity when t=0, calculate Q(0).
Since anything to the 0 is 1, it is 10/5730, or 1/573.
That works out in Excel to be 0.001745201.

(b) The amount after 2000 years when the half life is 5730 years would be using
t = 2000/5730 = 0.34904014 in the equation Q= 10(1/2)^(2000/5730).
I believe that gives Q=7.851062746.

The graph would be a curve that started at 10.
At x=5730, the curve would be at y=5.
At x=11460, the curve would be at y=2.5.
At 10,000 years, the value would be roughly 3.

As far as sketching the curve, just remember after every 5,730 years, the function would be half as high.  It would generate a curve that was concave up and had a limit of 0 as x went to infinity.

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Scott A Wilson

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I can answer any question in general math, arithetic, discret math, algebra, box problems, geometry, filling a tank with water, trigonometry, pre-calculus, linear algebra, complex mathematics, probability, statistics, and most of anything else that relates to math. I can also say that I broke 5 minutes for a mile, which is over 12 mph, but is that relevant?

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Experience in the area; I have tutored people in the above areas of mathematics for over two years in AllExperts.com. I have tutored people here and there in mathematics since before I received a BS degree back in 1984. In just two more years, I received an MS degree as well, but more on that later. I tutored at OSU in the math center for all six years I was there. Most students offering assistance were juniors, seniors, or graduate students. I was allowed to tutor as a freshman. I tutored at Mathnasium for well over a year. I worked at The Boeing Company for over 5 years. I received an MS degreee in Mathematics from Oregon State Univeristy. The classes I took were over 100 hours of upper division credits in mathematical courses such as calculus, statistics, probabilty, linear algrebra, powers, linear regression, matrices, and more. I graduated with honors in both my BS and MS degrees. Past/Present Clients: College Students at Oregon State University, various math people since college, over 7,500 people on the PC from the US and rest the world.

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My master's paper was published in the OSU journal. The subject of it was Numerical Analysis used in shock waves and rarefaction fans. It dealt with discontinuities that arose over time. They were solved using the Leap Frog method. That method was used and improvements of it were shown. The improvements were by Enquist-Osher, Godunov, and Lax-Wendroff.

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Master of Science at OSU with high honors in mathematics. Bachelor of Science at OSU with high honors in mathematical sciences. This degree involved mathematics, statistics, and computer science. I also took sophmore level physics and chemistry while I was attending college. On the side I took raquetball, but that's still not relevant.

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I earned high honors in both my BS degree and MS degree from Oregon State. I was in near the top in most of my classes. In several classes in mathematics, I was first. In a class of over 100 students, I was always one of the first ones to complete the test. I graduated with well over 50 credits in upper division mathematics.

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My clients have been students at OSU, people who live nearby, friends with math questions, and several people every day on the PC. I would guess that you are probably going to be one more.

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