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Answer :
To determine whether the given exponential function represents growth or decay, and to find the percentage rate of increase or decrease, we can follow these steps:
1. Identify the base of the exponential function:
The given function is [tex]\( y = 3700(0.97)^x \)[/tex].
2. Determine if it is growth or decay:
- Look at the base of the exponential, which is 0.97.
- If the base is greater than 1, it represents exponential growth.
- If the base is less than 1, it represents exponential decay.
Since 0.97 is less than 1, this indicates that the function represents exponential decay.
3. Calculate the percentage rate of decrease:
- To find the percentage rate, we consider how much the base is less than 1.
- Subtract the base from 1: [tex]\( 1 - 0.97 = 0.03 \)[/tex].
- Convert this decimal to a percentage by multiplying by 100: [tex]\( 0.03 \times 100 = 3\% \)[/tex].
Therefore, the function [tex]\( y = 3700(0.97)^x \)[/tex] represents a decay, with a 3% rate of decrease.
1. Identify the base of the exponential function:
The given function is [tex]\( y = 3700(0.97)^x \)[/tex].
2. Determine if it is growth or decay:
- Look at the base of the exponential, which is 0.97.
- If the base is greater than 1, it represents exponential growth.
- If the base is less than 1, it represents exponential decay.
Since 0.97 is less than 1, this indicates that the function represents exponential decay.
3. Calculate the percentage rate of decrease:
- To find the percentage rate, we consider how much the base is less than 1.
- Subtract the base from 1: [tex]\( 1 - 0.97 = 0.03 \)[/tex].
- Convert this decimal to a percentage by multiplying by 100: [tex]\( 0.03 \times 100 = 3\% \)[/tex].
Therefore, the function [tex]\( y = 3700(0.97)^x \)[/tex] represents a decay, with a 3% rate of decrease.
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