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## Exponential Inequalities

When will a bacteria colony reach a certain size? When will one investment outperform another? Many real-world models use exponential functions, and you'll need these tools to compare them.

# Exponential Inequalities Warmup

Which of these numbers is larger?

$\large A = \frac{2^8}{5^8} \hspace{0.3cm} \text{ , } \hspace{0.3cm} B = \frac{2^{7}}{5^{7}}$

What values of $$x$$ satisfy $\large 3^{x+ 2} < 3^{10}?$

What values of $$x$$ satisfy $\large \frac{3^{x+ 5}}{3^{11}} > 1?$

What values of $$x$$ satisfy $\large \left(\frac{1}{3}\right)^x < 3^{x+5}?$

True or False?

There is a real number $$x$$ such that $\large x < x^3 < x^4 < x^2.$

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