Suppose that the dollar value [tex]$v(t)$[/tex] of a certain house that is [tex]$t$[/tex] years old is given by the following exponential function:
[tex]$v(t)=476,000(0.87)^t$[/tex]
Answer (2)
The problem provides the exponential function v ( t ) = 476 , 000 ( 0.87 ) t representing the value of a house t years old. Since no specific question is asked, the function is analyzed.
Explanation
Analyzing the Given Function We are given the function v ( t ) = 476 , 000 ( 0.87 ) t which models the dollar value of a house that is t years old. The problem does not ask a specific question about this function. Therefore, without a specific question, we can only analyze the given function.
Examples
Understanding exponential decay is crucial in finance, such as calculating the depreciation of assets like cars or machinery. For instance, if a car's value decreases by 15% each year, we can use an exponential decay model to predict its value after a certain period. This helps in making informed decisions about when to sell or replace the asset, optimizing financial planning and minimizing losses.
The function v ( t ) = 476 , 000 ( 0.87 ) t models the depreciation of a house's value over time, where it retains 87% of its value each year. It can help determine the house's worth as it ages, enabling informed financial decisions. This function is key in understanding exponential decay in various financial contexts.
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