WEBVTT
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We're working on 1/2 life problem and we know the
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half life of the substance is five days. So
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if we start with 200 milligrams five days later,
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there's half of it. So there's 100 milligrams.
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Five days later, there's half of that 50 milligrams
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and five days later, half of that. So
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when 15 days have elapsed, there are 25 milligrams
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left. So that's the answer for part A.
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For part B. We want to generalize. So
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let's look at what's happening so that we can figure
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out how many milligrams will be left when T days
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have gone by. So we started with 200 then
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we multiply 200 by 1/2 so that could be considered
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multiplied by 1/2 to the first. And then we
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multiplied it by 1/2 again. So we multiplied it
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by 1/2 to the second power and then again,
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so we multiplied it by 1/2 to the third power
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. So what we can see is the exponents.
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Here is the number of days divided by five the
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number of days divided by the half life. So
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if we generalize that we could say that if T
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days have gone by, we have 200 times 1/2
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times the number of days divided by the half life
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, and that gives us our answer for Part B
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. Remember that T is in days now. We're
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going to use that as our formula or as our
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model, and we're going to find the estimated amount
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of bismuth to 10 left after three weeks, so
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three weeks would be 21 days. We need to
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convert today's since this whole problem has been done in
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days, and then we're going to substitute 21 into
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our equation for tea, and then we'll put it
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in the calculator and we get approximately 10.88 milligrams remaining
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. Finally, we'll use a graphing calculator, and
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we'll graph the function that we found 200 times,
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1/2 to the X, divided by five. And
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we'll also graph the line y equals one because we're
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interested in finding the time it takes to get down
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toe one milligram. So the line Y equals one
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will represent one milligram, then for a window.
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I've chosen to go from zero to our from negative
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1 to 80 on the X axis and from negative
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1 to 50 on my Y axis, and you
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just choose some numbers and fiddle around with them until
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you find what you like. Now we'll graph that
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. So here receive the exponential decay curve that represents
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the half life. And then we see this red
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line at the bottom. That is the line at
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a height of one that's one milligram and were interested
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in knowing that point of intersection so we can go
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into the calculate menu. Choose number five Intersect.
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Put the cursor on the first curve, press enter
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, put the cursor on the second curve, press
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enter and then move the cursor over to the intersection
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. Point press enter, and what we get you
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can see at the bottom of the screen is about
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38.2. So that tells us that it takes about
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38.2 days for the substance to be down to just
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one milligram remaining