Writing exponential functions | High School Math | Khan Academy

less than 1m read

·Nov 11, 2024

G is an exponential function with an initial value of -2. So, an initial value of -2 and a common ratio of 17th. Write the formula for G of T.

Well, the fact that it's an exponential function, we know that its formula is going to be of the form G of T is equal to our initial value, which we could call a, times our common ratio, which we could call R, to the T power. It's going to have that form. They tell us what the initial value is, it's -2. So this right over here is -2, and we know that the common ratio is 17th. So this is 17th.

So let me just write it again a little bit neater. G of T is going to be equal to our initial value -2 times our common ratio 17th to the T power. Hopefully, this makes sense.

The initial value is this number. Well, if T is equal to zero, then 17 to the zeroth power is 1, and so G of 0, you can view that time as being equal to zero if you view T as time, would be equal to -2. So that would be our initial value.

Then, if you think about every time you increase T by one, you're going to multiply by 17th again. So the ratio between successive terms is going to be 17th. And so that's why we call that the common ratio. Hopefully, you found that interesting.

Ecosystem dynamics: Clark’s nutcrackers and the white bark pine | Khan Academy

WTF Just Happened To California?!

View All

Apocalypse | A Pastor, A Rabbi and an Imam | The Story of God

Okay, so stop me if you’ve heard this one: a rabbi, a pastor, and an imam walk to a bar. Okay, so it wasn’t a bar; it was a diner to discuss my show, “The Story of God,” about the apocalypse. So the rabbi says, “Share with me a little bit about how the I…

Jacksonian Democracy part 2

So we’ve been talking about the emergence of Jacksonian Democracy in the first half of the 19th century in the United States. We’ve been talking about how, in this time period, the vote was slowly extended to all white male citizens so that by the end of …

You Are Immune Against Every Disease

You’re not a person; you’re a planet made of roughly 40 trillion cells. There is so much of you that if your cells were humanized, you’d be as big as 20 Mount Everest. For your creepy, cwy inhabitants, this makes your body an ecosystem rich in resources, …

What is risk and return? | Investments and retirement | Financial literacy | Khan Academy

So probably the main thing you will hear when you talk about investing is: What is the return that you got on your investment? Return on investment is often times, people will say ROI, and there’s a lot of different ways of calculating it. But maybe the m…

Consider THIS when navigating life's challenges

I hear so often that people say life can be difficult as though that’s an excuse for not being dealing with it well. Okay, so it’s difficult. So how do you approach it? Calm yourself down and then say, how does it work and how do I, uh, deal with it? One…

Lance Romance | Wicked Tuna

Who does this man? Is that Bubba? He’s got to learn to reel it without reeling it like that. Who did it? Lance romance? Really, Lance? Come here. It’s week nine, and Lance is still making rookie mistakes. I want Lance to learn these things because if he …

Writing exponential functions | High School Math | Khan Academy

More Articles