The value of electronics is falling

Question

The value of electronics is falling quite rapidly. A reasonable assumption is that the value halves every year. In this case, what is the percentage decrease in the value of an electronic good over four years? Round to the nearest percent

Answer 1

Hi Liana,

First, this problem is asking us to translate an English description of an equation into a mathematical equation.

We are given an unknown value, so we can use the variable x as a placeholder.

We also know that the number is losing half of its value every year, which is the same thing as multiplying that value by 1/2, or 0.5 every year. Lastly, we are also told to figure out how much the original value will have decreased over the period of 4 years.

If x is the starting value, after 1 year we will have

1/2 * x = x/2

The next year this value will be cut in half again

1/2 * x/2 = x/4

and again for the next year

1/2 * x/4 = x/8

and again for the next year

1/2 * x/8 = x/16

Since we are multiplying x by 1/2 4 times, this can also be written as,

1/2 * 1/2 * 1/2 * 1/2 * x = x/16

which can be simplified further to get

x(1/2)⁴ = x/16

This means that after 4 years, the value will be 1/16th of what it originally was. Since the question is asking how much was "lost", we can subtract the original value from the value after 4 years to get,

x/16 - x = -15x / 16

The negative sign represents that the value was lost. To convert 15/16 to a percentage, you first divide the values to get a decimal value and then multiply the decimal by 100%.

15/16 = 0.9375

0.9375 * 100% = 93.75%

and then the question is asking us to round to the nearest percent, so the final answer is,

94%

The value after 4 years decreased by 94%

I hope that helped!