Answer :
Final answer:
The given situation is an example of exponential decay in mathematics. Using the formula A = P(1 - r)^t, we can plug in the known values and solve for 't' using logarithms to get the number of years the game will depreciate to $3000.
Explanation:
The depreciation of the arcade game is an example of exponential decay, a concept in mathematics typically involving percentages and time. The formula for decay is A = P(1 - r)^t, with A being the final amount, P the initial amount, r the rate of decay, and t the time. We start with P, the initial cost of the arcade game which is $5000. The rate at which the game depreciates yearly is 8%, represented as 0.08 for our formula. Finally, we are asked when the game will reach a worth of $3000 which is our A. By substituting our known values into the formula, our equation will be: 3000 = 5000(1 - 0.08)^t. Solving for 't' using logarithms will give us the number of years.
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