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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 animal 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. And 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 3 days later, there's half of that left. That's 24.

Another 3 days, there's half of that. And finally another three days, that puts us at 12 days now, there are 6 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 4 hours. 4 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 5 p.m., . of the same day? So, we're gonna step 4 hours at a time. So we're gonna start at 9 a.m. We're gonna have 24 billion. 4 hours later, we multiply 24 by five halves.

Well cancelling the half, we get 12 times 5, that's 60. Then 4 hours later we're at 5 pm. 60 divided by half is 30. So that will be 150 billion. So at 5 pm of the same day, there are 150 billion, of these bacteria. If you happen to see a growth or decay problem, don't panic.

You will 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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