To buy a new computer for $2100, which decreases in value by 50% annually, when will the computer have a value of $600?

The computer will never reach an exact value of $600 dollars if the price only decreases annually, but after 2 years it will reach $525 The question at hand here is 2100÷2^× = 600. We need to find x. It can be done with trial and error, by just replacing x with different numbers until you get 600. Another way to work it out would be with logarithms, but by the way the question is phrased without an integer number, logarithms might be a bit too far for this.

Answered by lburke | 2024-06-10

It will take approximately 2.39 years , or about 2 years and 5 months , for the computer to be worth $600.
What is a percentage?
The percentage means the required value out of 100.
It is calculated by dividing the required value by the total value and multiplying by 100.
The percentage change is also calculated using the same method.
In percentage change we find the difference between the values given.
Example:
Required percentage value = a
total value = b
Percentage = a/b x 100
We have,
Since the computer decreases by 50% annually, it means that after one year, the value of the computer will be 50% of its original value, or 0.5 times the original value.
After two years ,
The value of the computer will be 50% of its value after one year, or (0.5)(0.5) times the original value, which is equivalent to 0.25 times the original value.
We can use this pattern to find how many years it will take for the computer to be worth $600.
Let x be the number of years it will take for the computer to be worth $600.
2100 x 0. 5 x = 600
Divide both sides by 2100:
0. 5 x = 600/2100
Simplify :
0. 5 x = 0.2857
Take the logarithm of both sides:
x log(0.5) = log(0.2857)
Solve for x:
x = log (0.2857) / log(0.5)
x ≈ 2.39
Therefore,
It will take approximately 2.39 years , or about 2 years and 5 months , for the computer to be worth $600.
Learn more about percentages here:
https://brainly.com/question/11403063
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Answered by swapnalimalwadeVT | 2024-06-24

The computer will take approximately 2.39 years to depreciate to a value of $600. This is calculated using the depreciation formula where the computer loses 50% of its value each year. Therefore, after about 2 years and 5 months, its value will reach $600.
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Answered by swapnalimalwadeVT | 2024-10-11