Question
Question 2 (1 point) Does this function represent exponential growth or exponential decay? \( y=45(.45)^{\mathrm{x}} \) \( \begin{array}{ll}\mathrm{a} & \text { Decay } \\ \mathrm{b} \quad \text { Growth }\end{array} \)
Ask by Marsh Flynn. in the United States
Feb 26,2025
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Answer
The function \( y = 45(0.45)^{x} \) represents **exponential decay**.
Solution
To determine whether the function \( y = 45(0.45)^{x} \) represents exponential growth or exponential decay, we need to analyze the base of the exponential term, which is \( 0.45 \).
1. **Identify the base**: The base of the exponential function is \( 0.45 \).
2. **Compare the base to 1**:
- If the base is greater than 1, the function represents exponential growth.
- If the base is between 0 and 1 (i.e., less than 1), the function represents exponential decay.
Since \( 0.45 < 1 \), this indicates that the function is decreasing as \( x \) increases.
Therefore, the function \( y = 45(0.45)^{x} \) represents **exponential decay**.
The correct answer is:
**a) Decay**.
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Simplify this solution Bonus Knowledge
This function represents exponential decay. To determine this, we can look at the base of the exponent, which is \(0.45\). Since this number is less than 1, it indicates that as \(x\) increases, \(y\) will decrease, showing a decline in the value of \(y\) over time. In terms of real-world applications, exponential decay can be seen in various fields like biology, where it describes processes such as population decline and radioactive decay of substances. For example, the amount of a radioactive material decreases over time, following a similar mathematical framework to this function.
