Carson invested $2000 in an investment account that earns 5% interest compounded continuously. How much money will she have in her account at the end of her 8th year of investing?

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Identify formula for continuous compounding: Identify the formula for continuous compounding. The formula for continuous compounding is given by $ A = P \cdot e^{rt} $, where: - $ A $ is the amount of money accumulated after n years, including interest. - $ P $ is the principal amount (the initial amount of money). - $ r $ is the annual interest rate (in decimal form). - $ t $ is the time the money is invested for in years. - $ e $ is the base of the natural logarithm, approximately equal to 2.71828.Plug in values: Plug in the values into the formula. Carson's initial investment ($ P $) is $2000, the annual interest rate ($ r $) is 5% or 0.05 in decimal form, and the time ($ t $) is 8 years. So, $ A = 2000 \cdot e^{0.05 \cdot 8} $.Calculate exponent part: Calculate the exponent part of the formula. $ 0.05 \cdot 8 = 0.4 $. Now, we have $ A = 2000 \cdot e^{0.4} $.Calculate value of e^0.4: Calculate the value of $ e^{0.4} $ using a calculator. $ e^{0.4} $ is approximately 1.49182.Calculate final amount: Calculate the final amount $ A $. $ A = 2000 \cdot 1.49182 $. $ A = 2983.64 $.

Carson invested $\$2000$ in an investment account that earns $5\%$ interest compounded continuously. How much money will she have in her account at the end of her $8$ th year of investing?

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Carson invested $\$2000$ in an investment account that earns $5\%$ interest compounded continuously. How much money will she have in her account at the end of her $8$ th year of investing?