4. a) Sketch the graphs of $y=2^x$ and $y={\left(\frac{1}{2}\right)}^x$ by completing the table of values. [
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b) Which one is exponential decay and which one is exponential growth? [
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Step 1 ：First, we need to understand the meaning of the question. The question asks us to sketch the graphs of two functions, $y=2^x$ and $y={\left(\frac{1}{2}\right)}^x$, and identify which one represents exponential growth and which one represents exponential decay.

Step 2 ：To sketch the graphs, we need to complete the table of values. We can choose a range of $x$ values and calculate the corresponding $y$ values for each function.

Step 3 ：For the function $y=2^x$, when $x$ is -2, -1, 0, 1, 2, the corresponding $y$ values are $\frac{1}{4}$, $\frac{1}{2}$, 1, 2, 4 respectively.

Step 4 ：For the function $y={\left(\frac{1}{2}\right)}^x$, when $x$ is -2, -1, 0, 1, 2, the corresponding $y$ values are 4, 2, 1, $\frac{1}{2}$, $\frac{1}{4}$ respectively.

Step 5 ：Next, we plot these points on the graph and draw the curves of the two functions.

Step 6 ：From the graphs, we can see that the function $y=2^x$ is increasing as $x$ increases, which means it represents exponential growth.

Step 7 ：Conversely, the function $y={\left(\frac{1}{2}\right)}^x$ is decreasing as $x$ increases, which means it represents exponential decay.

Step 8 ：Finally, we check our results. The graphs correctly represent the functions and correctly identify which function represents exponential growth and which represents exponential decay.