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.

The Body Deck

Video From Inside a Crocodile’s Mouth (Exclusive) | Expedition Raw

View All

Reading Habits of Warren Buffett and Charlie Munger

You know, I obviously recommend, first and foremost, “The Intelligent Investor,” with chapters 8 and 20 being the ones that you really should read. All of the important ideas in investing really are in that book because there are only about three ideas, a…

Dino Dig - Linked | Explorer

NARRATOR: Welcome to Moab, Utah, surrounded by thousands of square miles of Mars-like Red Rock landscape and the mighty Colorado River. Surprisingly, Utah has yielded fossils from more dinosaur species than any other state. And that fact alone makes for a…

Could Biking in a City Be Bad for Your Health? | National Geographic

Air pollution is bad for you, and we know that exercise is good for you. But there’s this unanswered question: is exercising in close proximity to traffic enough of a bad thing for you that we should be recommending separating biking lanes from traffic al…

The Last Days of the Romanovs | National Geographic

I think it’s a big tragedy, big tragedy for the country and for the world. For 300 years, the Romanovs ruled Russia as czars—loved, feared, revered, respected. But all too often, those who fly highest fall furthest. World War One brought Russia to revolut…

Separation of Powers and Checks and Balances

This is a great excerpt from Federalist 51 by James Madison. Just as a reminder, the Federalist Papers, which were written by Hamilton, Madison, and John Jay, were an attempt to get the Constitution passed, to get it ratified. So these were really kind of…

Limit of (1-cos(x))/x as x approaches 0 | Derivative rules | AP Calculus AB | Khan Academy

What we want to do in this video is figure out what the limit as ( x ) approaches ( z ) of ( \frac{1 - \cos(x)}{x} ) is equal to. We’re going to assume we know one thing ahead of time: we’re going to assume we know that the limit as ( x ) approaches ( 0 )…

Writing exponential functions | High School Math | Khan Academy

More Articles