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The formula \( A(t)=12,000 e^{(0.04) t} \) models the growth of an investment due to continuously compounded interest. What does \( t \) stand for? A the number of years since the initial investment B the amount after \( t \) years C the initial amount invested D the interest rate

Ask by Wade Johnson. in the United States
Jan 23,2025

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\( t \) stands for the number of years since the initial investment.

Solución

In the formula \( A(t) = 12,000 e^{0.04t} \): - **\( A(t) \)** represents the amount of money after time \( t \). - **12,000** is the initial investment (principal). - **0.04** is the annual interest rate (4%). - **\( t \)** stands for the time the money is invested or grows. **Therefore, \( t \) represents the number of years since the initial investment.** **Answer:** A the number of years since the initial investment

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Absolutely! The variable \( t \) in the formula represents the number of years since the initial investment was made. When you plug in values for \( t \), you can see how much your investment grows over time! It's like watching a little seed sprout and grow into a tree in your financial garden! Additionally, continuously compounded interest is a powerful concept that expresses how money can grow exponentially over time. Unlike traditional compounding, where interest is calculated at specific intervals, continuous compounding allows your investment to earn interest on interest seamlessly – hence, your money starts working faster! So, it's crucial to understand how time impacts your wealth-building journey!

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