Chapter 10: Q28. (page 528)

Determine whether the function $y = 2 {(4)}^{x}$ represents exponential growth or decay.

Short Answer

Expert verified

The given function $y = 2 {(4)}^{x}$ representsexponential growth.

Step by step solution

Step 1. Write down the given information.

The given function is $y = 2 {(4)}^{x}$ .

Step 2. Concept used.

The exponential function is of the form $y = a b^{x}$ represents exponential growth if the base role="math" localid="1648150066366" $b > 1$ and exponential decay if the base $0 < b < 1$ for all $a > 0$ .

Step 3. Explanation.

From the concept stated above it can be interpreted that the function $y = 2 {(4)}^{x}$ will represent exponential growth because the base (b) of the function $y = 2 {(4)}^{x}$ is such that $b > 1$ . Hence, the given function $y = 2 {(4)}^{x}$ represents exponential growth.

Step 4. Conclusion.

The given function $y = 2 {(4)}^{x}$ represents exponential growth.

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Determine whether the function $y = 2 {(4)}^{x}$ represents exponential growth or decay.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

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Short Answer

Step by step solution

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Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

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Determine whether the function $y = 2 {(4)}^{x}$ represents exponential growth or decay.