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Unit 2 lesson 8 exponents and exponential function sample work
A new Xbox series x video game console cost $535 and loses 10% of its value each year.
Write an exponential function that models the value of the video game console.
C = 535(0.90)^n where r=1+(-0.10)=0.90
c = cost = 535 * 0.90^n
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To write an exponential function that models the value of the video game console, we need to define the years and the corresponding value of the console.
Let's assume the initial value of the console is $535. Since it loses 10% of its value each year, the value after one year would be 90% of the previous year's value. Thus, the value after one year can be calculated using the formula:
Value after one year = $535 * 0.90
To generalize this for any year, we can raise 0.90 to the power of the number of years. Let's use the variable "t" to represent the number of years.
So, the exponential function that models the value of the video game console can be written as:
Value = $535 * (0.90)^t
In this function, "t" represents the number of years since the initial purchase of the console, and "Value" represents the current value of the console after "t" years.
Note: This function assumes that the console loses exactly 10% of its value each year, and there are no other factors influencing its depreciation. Additionally, it is important to note that this function only models the value based on the given rate of depreciation; actual market conditions may vary.