7b Is $$ y=2^{x} $$ an increasing function or a decreasing function?

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1. The function given is $$ y = 2^x $$. 2. An exponential function of the form $$ y = a^x $$ is increasing if $$ a > 1 $$ and decreasing if $$ 0 < a < 1 $$. 3. In this case, the base is $$ 2 $$, and since $$ 2 > 1 $$, the function $$ y = 2^x $$ is an increasing function. 4. Another way to see this is by considering the derivative. The derivative of $$ y = 2^x $$ with respect to $$ x $$ is: $$ y' = 2^x \ln 2 $$ Since $$ 2^x > 0 $$ for all $$ x $$ and $$ \ln 2 > 0 $$, we have $$ y' > 0 $$ for all $$ x $$. 5. Therefore, the function is increasing for all values of $$ x $$. The answer is: $$ y = 2^x $$ is an increasing function. $$ y = 2^x $$ is an increasing function.

7b Is an increasing function or a decreasing function?

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