# How To Solve Radioactive Decay Problems Her studies are focused on proteins and neurodegenerative diseases.

Her studies are focused on proteins and neurodegenerative diseases.

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We don't see it, but there's a 1 there, times 100.

In the second hour, 0.965 to the second power, times 100. This is now 2 years after 1999, and you're going to grow 8% from this number. The answer to our question will be 200 times 1.08 to the eighth power.

I could simplify this to a decimal approximation, but I won't, because I don't want to introduce round-off error if I can avoid it.

So, for now, the growth constant will remain this "exact" value.

So in general, in the nth hour-- let me do this in a nice bold color-- in the nth hour, we're going to have 0.965 to the nth power, times 100 left of our radioactive substance. Then in 2000, which is 1 year after 1999, how many is she going to be operating? So she'll be operating all the stores that she had before plus 8% of the store she had before. And you're going to see, the common ratio here is 1.08. Well, this is just 1 times 200 plus 0.08, times 200. You're going to multiply 1.08 times that number, times 1.08 times 200. If, after n years after 1999, it's going to be 1.08-- let me write it this way. 0 years, this is the same thing as a 1 times 200, which is 1.08 to the zeroth power. Let's get our calculator out and calculate it.

And oftentimes you'll see it written this way. So we have, Nadia owns a chain of fast food restaurants that operated 200 stores in 1999. And let's talk about how many stores Nadia is operating, her fast food chain. If you're growing by 8%, that's equivalent to multiplying by 1.08. It's going to be 200 times 1.08 to the nth power. So they're asking us, how many stores does the restaurant operate in 2007? So we want to figure out 200 times 1.08 to the eighth power.

No matter the particular letters used, the green variable stands for the ending amount, the blue variable stands for the beginning amount, the red variable stands for the growth or decay constant, and the purple variable stands for time.

Get comfortable with this formula; you'll be seeing a lot of it.

You have your initial amount times your common ratio, 0.965 to the nth power. Well, we're going to have 100 times 0.965 to the sixth power left. If the rate of increase is-- oh actually, there's a typo here, it should be 8%-- the rate of increase is 8% annually, how many stores does the restaurant operate in 2007? She's going to be operating 370 restaurants, and she'll be in the process of opening a few more.

This is how much you're going to have left after n hours. And we could use a calculator to figure out what that is. So we have 100 times 0.965 to the sixth power, which is equal to 80.75. So if we round it down, she's going to be operating 370 restaurants.

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