Find the cost of each item in 13 years, assuming an inflation rate of \( 12 \% \) (compounded continuously). (Round your answers to the nearest cent.) (a) phone bill, \( \$ 33 \) \( \$ \) (b) pair of shoes, \( \$ 62 \) \( \$ \) (c) new suit, \( \$ 338 \) \( \$ \) (d) monthly rent, \( \$ 700 \) \( \$ \)

To find the future cost of each item considering continuous compounding due to inflation, we can use the formula for continuous compounding: \[ A = Pe^{rt} \] where: - \( A \) is the amount of money accumulated after time \( t \), - \( P \) is the principal amount (initial cost), - \( e \) is Euler's number (approximately 2.71828), - \( r \) is the annual interest rate (in decimal), - \( t \) is the time (in years). Given the inflation rate \( r = 0.12 \) and \( t = 13 \), we can calculate it for each item. (a) Phone bill: \[ A = 33e^{0.12 \times 13} \approx 33 \times e^{1.56} \approx 33 \times 4.769 = 157.37 \] \( \$ 157.37 \) (b) Pair of shoes: \[ A = 62e^{0.12 \times 13} \approx 62 \times e^{1.56} \approx 62 \times 4.769 = 295.73 \] \( \$ 295.73 \) (c) New suit: \[ A = 338e^{0.12 \times 13} \approx 338 \times e^{1.56} \approx 338 \times 4.769 = 1618.47 \] \( \$ 1618.47 \) (d) Monthly rent: \[ A = 700e^{0.12 \times 13} \approx 700 \times e^{1.56} \approx 700 \times 4.769 = 3338.38 \] \( \$ 3338.38 \) So the future costs are: (a) phone bill: \( \$ 157.37 \) (b) pair of shoes: \( \$ 295.73 \) (c) new suit: \( \$ 1618.47 \) (d) monthly rent: \( \$ 3338.38 \)