Now, what is h of one going to be equal to? It's going to be one-fourth times two to the first power. For example, h of, let me do this in that green color, h of zero is equal to, we alreadyĮstablished one-fourth. Integer inputs into it, you would see a pattern. Integer inputs into this, especially sequential And in my brain, we say well why is itĬalled a common ratio? Well, if you thought about Now, you might be saying, well what do we call this number? What do we call that number there? Or that number there? And that's called the common ratio. Hopefully that makes sense, but since you're looking at it, hopefully it does make a little bit. In for the exponent, then the number raised to the exponent is just going to be one, and you're just going to be left with that thing that you're Your initial value, well if you put a zero So the initial value is once again, that. So, if we look at its intial value, f of zero is going to be five times three to the zero power and, the same thing again. We have the initial value times some number to this exponent. So the initial value,Īt least in this case, it seems to just be that number that sits out here.
Well, two to the zero power, is just one. And when we evaluate that, that's going to be one-fourth times two to the zero. So, for in these cases, the initial value for the function, h, is going to be, h of zero. The value of the function when the input is zero. Used to the terminology, so one thing that you might see is a notion of an initial value. In fact, we'll explore many of them, but I'll get a little Interesting things to think about in exponential function. Once again, this is an exponential function. I could write, f of, let's say the input is a variable, t, is equal to is equal to five times times three to the t. I could write anotherĮxponential function. Exponential function, and that's because the variable, the input into our function, is sitting in its definition of what is the output of And a function like this isĬalled an exponential function. So, first of all, you might notice something Let's say, h of n is equal to one-fourth times two to the n.
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