Question 1 (3 points) For graduation, Emma receives \( \$ 875 \) from the money in the cardes she received from family and friends. If she invests it in an account that earns \( 6 \% \) interest compounded continuously, how much will this money be worth in 3 years? 2.) Write the equation (how you will set it up through substitution): ***Be sure to use parenthesis to show what all is included in the exponent. 3.) After 3 years, Emma will have will be \( \$ \) in her account. (round to the nearest whole dollar)

To find out how much Emma's investment will be worth in 3 years with continuous compounding, we can use the formula for continuous compounding: \[ A = Pe^{rt} \] 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 (decimal). - \( t \) is the time the money is invested or borrowed for, in years. - \( e \) is the base of the natural logarithm, approximately equal to 2.71828. Using the given values: 1. **Substituting the known values:** - \( P = 875 \) - \( r = 0.06 \) (which is \( 6\% \) as a decimal) - \( t = 3 \) The setup through substitution will look like this: \[ A = 875 \cdot e^{(0.06 \cdot 3)} \] 2. **Calculate the final amount:** - First calculate the exponent: \( 0.06 \cdot 3 = 0.18 \). - Now substitute it back: \[ A = 875 \cdot e^{0.18} \] Using \( e^{0.18} \approx 1.1972 \): \[ A \approx 875 \cdot 1.1972 \approx 1041.05 \] So, after rounding to the nearest whole dollar, Emma will have approximately \( \$ 1,041 \) in her account after 3 years.