Chapter 10: Q1. (page 527)

Give an example of a value of $b$ for which $y = b^{x}$ represents exponential decay.

Short Answer

Expert verified

The required exponential decay function is $y = {(\frac{4}{5})}^{x}$ where the value of $b = \frac{4}{5}$ .

Step by step solution

Step 1. Write down the given information.

The given function is $y = b^{x}$ .

Step 2. Concept used.

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

Step 3. Explanation.

From the concept stated above it can be interpreted that the function $y = b^{x}$ will represent exponential decay if the value of base (b) of the function $y = b^{x}$ is such that $0 < b < 1$ . Hence consider $b = \frac{4}{5}$ and plug it in $y = b^{x}$ .

Therefore, $y = {(\frac{4}{5})}^{x}$ is the required exponential decay function where the value of $b = \frac{4}{5}$

Step 4. Conclusion.

The required exponential decay function is $y = {(\frac{4}{5})}^{x}$ where the value of $b = \frac{4}{5}$ .

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Give an example of a value of $b$ for which $y = b^{x}$ represents exponential 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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Give an example of a value of b for which y=bxrepresents exponential decay.

Short Answer

Step by step solution

Step 1. Write down the given information.

Step 2. Concept used.

Step 3. Explanation.

Step 4. Conclusion.

One App. One Place for Learning.

Most popular questions from this chapter

Recommended explanations on Math Textbooks

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Study anywhere. Anytime. Across all devices.

Give an example of a value of $b$ for which $y = b^{x}$ represents exponential decay.