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.

Worked example: Finding the formula of an ionic compound | AP Chemistry | Khan Academy

Erin McCoy and Kevin O'Leary discuss cottages and mortgages

View All

See How Life Has Changed in the Middle East Over 58 Years | Short Film Showcase

That’s right across the Lebanese Syrian border. I stopped, pulled out my camera because I had resolved that the entire time I was in the Middle East, that I was going to keep a detailed photographic record of all my landscapes and have a real collection o…

The On, Off Switch of Consciousness | Breakthrough

To map what goes on inside the brain, Muhammad implants tiny electrodes in his patients’ skulls. He then sends pulses to these electrodes, gradually increasing the current, sometimes with dramatic results. Recently, he inserted an electrode next to a smal…

Comparative advantage - output approach | Basic economic concepts | Microeconomics | Khan Academy

In this, in the next video, we’re going to learn how to calculate opportunity costs and determine who has the comparative advantage in a goods production using data from both an output table and an input table. If we look at our PPCs in the graph on the l…

Composite functions to model extraterrestrial skydiving

We’re told that Phlox is a skydiver on the planet Lernon. The function A of w is equal to 0.2 times w squared, which gives the area A in square meters under Flux’s parachute when it has a width of w meters. That makes sense. The function V of A is equal t…

Democratic ideals in the preamble of the US Constitution

This over here is a picture of the Constitutional Convention, which we mentioned happened in 1787. The original intent of the Constitutional Convention was to revise the Articles of Confederation, but folks like Alexander Hamilton and James Madison really…

Q&A With Grey: Meme Edition

Hello Internet. It’s Q&A time. First question: “Are memes the future of society?” I think you meant this as a joke, but the answer is yes. The internet, for memes, is the perfect petri dish, gladiatorial theater, and mutation chamber… growing, selecti…

Writing exponential functions | High School Math | Khan Academy

More Articles