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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?).

Which of the following could be the graph of \( y = - \frac{1}{a^x}, \) if \( a>1 ? \)

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The graph of \(y = 5^{-x + 3} + 7^{-x - 1} + 6\) never goes below the line \(y = k.\)

What is the largest possible value of \(k\) such that the statement above is true?

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Shown above is the graph of \( y = f(x) ,\) which is the reflection of \( y = 2^{2x+a} + b \) in the \( y \)-axis. If the graph of \( y = f(x) \) passes through \( (-1, 10) \) and the equation of the graph's asymptote is \( y=2 \), what is \(a+b\)?

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