A video game costs \( \$ 60 \) today. It the inflation rate is \( 4.75 \% \) and is compounded continuously how much will this same video game cost in 5 years? Round your answer to the nearest cent (hundredth).

To find the cost of the video game in 5 years with continuous compounding, we can use the formula for continuous compounding: \[ A = P \times e^{r \times t} \] Where: - \( A \) is the amount after time \( t \), - \( P \) is the principal amount (initial cost), - \( r \) is the annual interest rate (in decimal form), - \( t \) is the time in years. Given: - Initial cost of the video game today: \( P = \$60 \) - Inflation rate: \( r = 4.75\% = 0.0475 \) (in decimal form) - Time: \( t = 5 \) years Substitute the values into the formula: \[ A = 60 \times e^{0.0475 \times 5} \] Now, we can calculate the cost of the video game in 5 years using the formula for continuous compounding. Calculate the value by following steps: - step0: Calculate: \(60e^{0.0475\times 5}\) - step1: Multiply the numbers: \(60e^{0.2375}\) - step2: Convert the expressions: \(60e^{\frac{19}{80}}\) - step3: Rewrite the expression: \(60\sqrt[80]{e^{19}}\) The cost of the video game in 5 years with continuous compounding is approximately $76.08. Rounding to the nearest cent (hundredth), the cost will be $76.08.