examples, and problems from the community.

including olympiad champions, researchers, and professionals.

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

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From compound interest to bubonic plague, things that grow or spread really fast are often modeled by exponential functions. Learn about these powerful functions (pun intended?).

What is the value of \(\dfrac{6^5}{6^3}\) ?

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by **Brilliant Staff**

True or false: \((-2)^{3} = 2^{-3}\) ?

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by **Brilliant Staff**

\[f(x) = x^{100}\] \[g(x) = 100^{x}\]

Which is bigger, \(f(10000)\) or \(g(10000)\) ?

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\(f\) is an exponential function such that \(f(x) = K(2^{x})\) for some constant \(K\).

If \(f(10) = 2000\) and \(f(a) = 500\), what is the value of \(a\) ?

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\[\Large 8^{2n} = 4^{n^2}\]

What is the value of \(n\)?

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by **Brilliant Staff**

© Brilliant 2017

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