You hear on the news that over the next 5 years, the inflation rate will skyrocket to \( 12 \% \). If today a new Blu-ray movie costs \( \$ 19.99 \), assuming continuous compounding, how much will that same disk cost in 5 years? Round your answer to the nearest cent (hundredth).

To calculate the future cost of the Blu-ray movie considering an inflation rate of 12% compounded continuously, you 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 number of years the money is invested or borrowed for, - \( e \) is the base of the natural logarithm (approximately equal to 2.71828). In this case: - \( P = 19.99 \) - \( r = 0.12 \) - \( t = 5 \) Plugging in the values: \[ A = 19.99 \times e^{0.12 \times 5} \] \[ = 19.99 \times e^{0.6} \] \[ \approx 19.99 \times 1.8221 \quad (\text{using } e^{0.6} \approx 1.8221) \] \[ \approx 36.42 \] So, the cost of the Blu-ray movie in 5 years will be approximately **\$36.42**.