Find the cost of each item in 10 years, assuming an inflation rate of \( 9 \% \) (compounded continuously). (Round your answers to the nearest cent.) (a) movie admission, \( \$ 7.00 \) \( \$ \) (b) CD, \( \$ 13.95 \) \( \$ \) (c) textbook, \( \$ 140.00 \) \( \$ \) (d) electric bill, \( \$ 125 \) \( \$ \)
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To find the future cost of each item considering a continuous inflation rate of \( 9\% \), you 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 (the initial cost), \( r \) is the rate of inflation, and \( t \) is the time in years. Let's calculate each item: (a) For the movie admission: \[ A = 7.00 \times e^{0.09 \times 10} \approx 7.00 \times e^{0.9} \approx 7.00 \times 2.4596 \approx 17.23 \] So, the cost of movie admission in 10 years will be approximately \( \$ 17.23 \). (b) For the CD: \[ A = 13.95 \times e^{0.09 \times 10} \approx 13.95 \times e^{0.9} \approx 13.95 \times 2.4596 \approx 34.31 \] Thus, the cost of the CD in 10 years will be approximately \( \$ 34.31 \). (c) For the textbook: \[ A = 140.00 \times e^{0.09 \times 10} \approx 140.00 \times e^{0.9} \approx 140.00 \times 2.4596 \approx 344.34 \] Therefore, the cost of the textbook in 10 years will be approximately \( \$ 344.34 \). (d) For the electric bill: \[ A = 125.00 \times e^{0.09 \times 10} \approx 125.00 \times e^{0.9} \approx 125.00 \times 2.4596 \approx 307.45 \] So, the cost of the electric bill in 10 years will be approximately \( \$ 307.45 \). Final rounded costs are: (a) \( 17.23 \) (b) \( 34.31 \) (c) \( 344.34 \) (d) \( 307.45 \)
