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# Exponential Decay

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Exponential decay refers to an amount of substance decreasing exponentially. Exponential decay is a type of exponential function where instead of having a variable in the base of the function, it is in the exponent. Exponential decay and exponential growth are used in carbon dating and other real-life applications.

So exponential growth and decay refers to an amount of substance either growing or decreasing exponentially.

So what the formula your book is typically going to be using is this N is equal to N with this little 0 E to the RT. What this N is you can either hear it N 0 or N sub 0. Either way basically it's your initial amount.

In general I tend not to be so fond of this equation because it's just another equation for me to memorize. What I want to do is draw some comparisons how it's exactly the same thing as our PERT equation which we'll use for compounded continuously interest.

So basically what we have is N 0 or N sub 0 as our initial amount which corresponds directly to P which is our principal or initial amount. We have E to the RT. Those are exactly the same. Rate isn't exactly as it was like with a percent like we want to have interest that's 4. .04 goes in. It's a little bit more abstract. Little bit typically a complicated number but still a rate that relates to this problem.

T is still time for our exponential growth. It could vary, be in days, hours, whatever it is. But it's still just a time. This term by itself on the left is going to be the ending amount. Okay.

So it's another equation but it's really the exact same thing as PERT which we already know. The one other thing we need to talk about is distinction between exponential growth and decay. That's really easy as well.

Exponential growth means something is getting bigger. You think of the whole scenario with rabbits multiplying rapidly, that's exponential growth. Okay.

And how that actually pans out is if this R, this rate is going to be positive, then our terms are growing. We're getting bigger. If this R is negative, then our terms are going to be getting smaller. That will be decay.

So exponential growth and decay. It's a different formula. But it's really exactly the same as our PERT formula, just some different letters thrown in the mix.

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