To determine the initial value, we need to make some assumptions based on the relationship between the years and the amounts listed in the table.
It seems like we might have a list of amounts after a certain number of years, but it's unclear what year corresponds to which amount based on the data provided. However, let's break it down based on typical scenarios in finance.
If we assume the amounts are the total after each year, you can denote them as follows:
- After Year 0 (initial value): \( P \) (unknown initial value)
- After Year 1: \( 1,080 \)
- After Year 2: \( 1,160 \)
- After Year 3: \( 1,240 \)
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From Year 1 to Year 2: \[ 1,160 - 1,080 = 80 \]
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From Year 2 to Year 3: \[ 1,240 - 1,160 = 80 \]
This indicates that there is a consistent increase of $80 each year.
Now, to find the initial value (Year 0), we can work backwards from Year 1: \[ 1,080 - 80 = 1,000 \]
So the initial value (after Year 0) is \( \boxed{1,000} \).