In the formula you provided for compound interest:
\[ A = 200\left(1 + \frac{0.08}{1}\right)^{1 \cdot t} \]
we can simplify this to:
\[ A = 200(1.08)^t \]
This resembles the general formula for exponential growth:
\[ y = a(1 + r)^t \]
where:
- \( a \) is the initial amount (the principal),
- \( r \) is the rate of growth,
- \( t \) is time.
In your compound interest formula, the components compare as follows:
- The initial amount \( a \) corresponds to 200.
- The growth factor \( r \) corresponds to 0.08 (which represents an 8% interest rate).
- The variable \( t \) is time, which remains the same in both formulas.
Thus, in this context, the part of the compound interest formula that compares best with the variable \( t \) is \( t \) itself, as both expressions indicate the same concept of time passing for the growth of the investment or account.
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