Final answer:
The function V(t)=5200(0.6)ᴇ is used to calculate the depreciation of office equipment over time, with the value decreasing annually by 40%. To find the equipment's value at any time t, this value is plugged into the function. Comparing the depreciated value with the selling price will indicate a profit or loss.
Step-by-step explanation:
The business estimates that the value V(t) of office equipment is decreasing according to the function V(t)=5200(0.6)ᴇ, where t represents the number of years that have elapsed since the equipment was purchased. This type of function is an exponential decay model often used in depreciation calculations. The base of the exponential, 0.6, represents the annual rate of depreciation, meaning that the value of the equipment decreases by 40% each year.
Calculating Depreciation Over Time
To calculate how much the office equipment will be worth after a certain number of years, t, you simply plug the value of t into the function. For example, if you want to find the value after 3 years, calculate V(3) = 5200(0.6)³.
Evaluating Profit or Loss from Selling Equipment
In the context of making a decision about selling the equipment, such as if the company decides to sell the computers for $500, the company can determine whether there is a profit or loss by comparing the selling price to the depreciated value of the equipment. For example, if after two years the value according to the function is less than $500, selling it at $500 would mean a profit is being made.