Consider the exponential function . If the function shows exponential decay and the value of when is , find the value of . Write your answer in the blank: b = ________.
Answer & Analysis
Analysis
Question Analysis
This question tests the understanding of exponential decay and the ability to solve for the base given a specific value of at a certain . The key is to recognize that 0 < b < 1 for exponential decay.
Key Concept Explanation
Exponential decay occurs when the base is between 0 and 1. The function decreases as increases. Given a specific value of at a certain , we can solve for by substituting the values into the function.
Step-by-step Solution
1. Substitute the given point (3, ) into the function
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