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Growth and Decay
Growth and Decay. Some word problems concern populations or samples that are in the process of growth or decay. Human populations and populations of animals or bacteria experience natural growth. Decay can include radioactive decay, something melting, a bacteria population getting wiped out, etc.
This is an extremely rare question type, so chances are relatively low that you will see this question. An another important idea. These questions may refer to some specialized scientific ideas, such as radioactive decay.
You do not need to know anything about the underlying science. All the mathematical information you will need will be given in the question itself. The basic format of this question is you will be given some starting value and told that the size gets multiplied or divided by a certain quantity in some fixed interval of time. Then you will be asked for the resultant amount after some slightly longer period of time.
Take the calculations one change interval at a time. Whatever, whatever time interval they give in the question, use that time interval as a step. And just move by those steps. Step by step, figure out the amounts until you arrive at the final amount. Here’s a practice question.
Pause the question and then we’ll talk about this. Okay. When isotope QXW radioactively decays, it loses exactly half its mass in each three-day period. So that’s our step interval, three days.
Suppose scientists start with a 96 gram sample of a pure isotope of this on a certain day. What will be the remaining mass in 12 days? So step by step we’ll, we’ll move. So at the start, we have 96 grams. Three days later, there’s half of this left.
So there’s 48 left. Another three days later, there’s half of that left that’s 24. Another three days, there’s half of that. And finally, another three days that puts us at 12 days now. There are six grams left and that’s the answer. Here’s another problem.
Pause the video and then we’ll talk about this. Okay. So we have some kind of bacteria and it multiplies the size of its population by five and a half by five-halves every four hours. Four hours is the, is the time interval step that we’re gonna take.
So there are 24 billion at 9 a.m. And optimal conditions are maintained. How many are there at five p.m. Of the same day? So, we’re gonna step four hours at a time. So we’re gonna start at 9 a.m.
We’re gonna have 24 billion four hours later, we multiply 24 by five-halves. We’ll cancelling the half we get 12 times 5, that’s 60. Then four hours later, we’re at 5 p.m. 60 divided by a half is 30, so that will be 150 billion. So at 5 PM the same day there are 150 billion of this bacteria. If you happen to see a growth or decay problem, don’t panic.
You will be given the multiplier you need and all you need to do is follow the calculations step by step, one change interval at a time.
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