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# Exponential Functions

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?).

examples, and problems from the community.

including olympiad champions, researchers, and professionals.

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

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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