The function \( B(t) = 2500 \left( \frac{21}{20} \right)^t \) describes the growth of Dewayne's investment over time. Let's break down the components of this function:
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Initial Investment: Dewayne initially invested $2500. This is represented by the coefficient in the function.
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Growth Rate: The term \( \left( \frac{21}{20} \right)^t \) indicates the growth of the investment over time. The base \( \frac{21}{20} \) is greater than 1, which means the investment is growing. Specifically, \( \frac{21}{20} \) is equal to 1.05, indicating a growth rate of 5% per year.
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Elapsed Time (t): The variable \( t \) represents the number of years that have passed since Dewayne made the investment.
Key Points to Note:
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Calculating the Value of the Investment: To find the total amount of money in the account after a specific number of years, you can substitute the value of \( t \) into the function.
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Example Calculation: If you want to find out how much money Dewayne will have after 5 years, substitute \( t = 5 \):
\[ B(5) = 2500 \left( \frac{21}{20} \right)^5 \]
To compute this:
\[ B(5) = 2500 \left( 1.05 \right)^5 \approx 2500 \times 1.27628 \approx 3190.70 \]
So after 5 years, Dewayne will have approximately $3190.70.
If you have any further questions or need specific calculations or scenarios analyzing Dewayne's investment, feel free to ask!