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4. Communicate Precisely How are exponential growth functions similar to exponential decay functions? How are they different?

4. Communicate Precisely How are exponential growth functions similar to exponential decay functions? How are they different?

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### Question 4: Communicate Precisely #### Description: In this exercise, you are asked to compare and contrast exponential growth functions with exponential decay functions. Reflect on their similarities and differences. #### Question: **Communicate Precisely** How are exponential growth functions similar to exponential decay functions? How are they different? #### Input Area: You will find a text box where you can enter your answer. Use this space to explain your understanding of the topic. #### Action Button: - **CHECK ANSWER**: When you have finished writing your response, click this button to submit your answer for review. ### Instructions for Students: - Think about the general characteristics of exponential functions. - Consider how the mathematical expressions for growth and decay functions differ. - Reflect on the significance of the base of the exponential function being greater than 1 versus being between 0 and 1. #### Example Explanation: - **Similarities**: Both exponential growth and decay functions can be modeled using the equation \( y = ab^x \), where \( a \) is the initial value and \( b \) is the base of the exponential. - **Differences**: In exponential growth functions, the base \( b \) is greater than 1, which causes the value to increase over time. In exponential decay functions, the base \( b \) is between 0 and 1, which causes the value to decrease over time.
Transcribed Image Text:### Question 4: Communicate Precisely #### Description: In this exercise, you are asked to compare and contrast exponential growth functions with exponential decay functions. Reflect on their similarities and differences. #### Question: **Communicate Precisely** How are exponential growth functions similar to exponential decay functions? How are they different? #### Input Area: You will find a text box where you can enter your answer. Use this space to explain your understanding of the topic. #### Action Button: - **CHECK ANSWER**: When you have finished writing your response, click this button to submit your answer for review. ### Instructions for Students: - Think about the general characteristics of exponential functions. - Consider how the mathematical expressions for growth and decay functions differ. - Reflect on the significance of the base of the exponential function being greater than 1 versus being between 0 and 1. #### Example Explanation: - **Similarities**: Both exponential growth and decay functions can be modeled using the equation \( y = ab^x \), where \( a \) is the initial value and \( b \) is the base of the exponential. - **Differences**: In exponential growth functions, the base \( b \) is greater than 1, which causes the value to increase over time. In exponential decay functions, the base \( b \) is between 0 and 1, which causes the value to decrease over time.
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