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.

Filming the Alaskan Wilds - Behind the Scenes | Life Below Zero

STOIC PRINCIPALS ON HOW TO MAKE THEM MISS YOU BADLY | STOICISM INSIGHTS

View All

Testing a Shark Deterrent | Shark Beach with Chris Hemsworth

I think it’s fair to say, however good we get at keeping humans and sharks apart in the ocean, there will always be moments when we meet. In those worst-case scenarios when sharks bite, is there anything that can be done? Charlie Houveneers is a scientis…

Basic derivative rules (Part 1) | Derivative rules | AP Calculus AB | Khan Academy

So these are both ways that you will see limit-based definitions of derivatives. Usually, this is if you’re thinking about the derivative at a point. Here, if you’re thinking about the derivative in general, but these are both equivalent. They’re both bas…

How To Unmask The Narcissist's Double Life | STOICISM

Have you ever felt like someone could see right through you, tapping into your deepest fears and desires, and manipulating them to their own advantage? Imagine living in a world where your very emotions are the plaything of a master illusionist, someone w…

TIL: Why Mars's Ocean Disappeared | Today I Learned

This is what Mars looks like today, and this is what it may have looked like 3 to 3.5 billion years ago. Notice the difference? Well, the planet was warmer and wetter, and it even had an ocean that covered the entire Northern Hemisphere. So where did that…

Ample reserves regime | AP Macroeconomics | Khan Academy

What we’re going to do in this video is talk about some interesting things that have happened since 2008. In particular, we’re going to talk about what an ample reserves regime is but even more importantly what its actual implications are and how you can …

15 Biggest Threats to Your Financial Security

Have you ever felt like your financial security was walking a tightrope? It can feel like any small gust of wind, a sudden expense, a job hiccup, or an unexpected twist in life could throw everything out of balance. But what if you could see those gusts o…

Writing exponential functions | High School Math | Khan Academy

More Articles