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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.

(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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