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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?).

Level 3

         

\[ \Huge \sqrt{\color{red}9^{\color{green}{16} \color{blue}{x^2}}} \]

Which of the following is equal to the above expression?

\[ \large A = 2^{5555}, \qquad B = 3^{3333}, \qquad C = 6^{2222} \]

What is the order of these numbers from smallest to largest?

If \( 2^x = 3^y = 6,\) then which of the following statements is true?

Find the sum of all integer solutions to the equation

\[\large (x^2 - 3x + 1)^{x + 1} = 1.\]

If you have a piece of paper that is \(0.1\text{ mm}\) thick, then how many times will you have to fold it in half in order for it to become tall enough to reach the moon?

Note: The distance from the earth to the moon is \( 384400\text{ km}\).

You have to round off the answer that you are getting to get the answer that you will enter in the answer box.

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