Final answer:
To calculate the cost of the TV after five years with a 2.5% annual decrease, we use the formula for exponential decay. The calculation shows that the TV will cost approximately $884.74, which does not match any of the options provided, suggesting an error in the answer choices.
Step-by-step explanation:
The student asked how much a TV that costs $1000 today will cost in five years if the price is decreasing at a rate of 2.5% per year. To find the cost after five years, we use the formula for exponential decay, which is: Future Value = Present Value * (1 - rate)^time. In this case, the Present Value is $1000, the rate is 2.5% or 0.025, and the time is 5 years.
Plugging these values into the formula gives us:
Future Value = $1000 * (1 - 0.025)^5.
Future Value = $1000 * (0.975)^5.
Future Value = $1000 * 0.884736.
Future Value = $884.74
Therefore, the cost of the TV in five years will be approximately $884.74, which is not listed in the options provided. The closest answer choice would be D: $783.74, but this is incorrect based on the calculation.