Set up the formula to find the balance after 8 years for a total of $$ \$ 12,000 $$ invested at an annual interest rate of $$ 9 \% $$ compounded continuously. $$ A=12,000\left(1+\frac{9}{365}\right)^{(365)(8)} $$ $$ A=12,000(e)^{(0.09)(8)} $$ $$ A=12,000\left(1+\frac{0.09}{365}\right)^{(365)(8)} $$ $$ A=12,000(e)^{(9)(8)} $$

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To find the balance after 8 years for a total of $12,000 invested at an annual interest rate of 9% compounded continuously, we can use the formula for continuous compounding:

$$ A = P \times e^{r \times t} $$

Where:
- $$ A $$ is the balance after $$ t $$ years,
- $$ P $$ is the principal amount (initial investment),
- $$ r $$ is the annual interest rate,
- $$ t $$ is the time in years.

Given:
- $$ P = \$12,000 $$
- $$ r = 9\% = 0.09 $$
- $$ t = 8 $$ years

Substitute the values into the formula:

$$ A = 12,000 \times e^{0.09 \times 8} $$

$$ A = 12,000 \times e^{0.72} $$

Now, we can calculate the balance after 8 years using the formula.
Calculate the value by following steps:
- step0: Calculate:
  $$12000e^{0.72}$$
- step1: Convert the expressions:
  $$12000e^{\frac{18}{25}}$$
- step2: Rewrite the expression:
  $$12000\sqrt[25]{e^{18}}$$
The balance after 8 years for a total of $12,000 invested at an annual interest rate of 9% compounded continuously is approximately $24,653.20.
The balance after 8 years is calculated using the formula $$ A = 12,000 \times e^{0.09 \times 8} $$, which equals approximately \$24,653.20.

Set up the formula to find the balance after 8 years for a total of invested at an annual
interest rate of compounded continuously.

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Set up the formula to find the balance after 8 years for a total of invested at an annual interest rate of compounded continuously.