If the cost of a cell phone has decreased 20% a year during the past 10 years, does that correspond to a cost decrease of 200%? Explain your answer as though you were talking to someone who has never taken algebra.
No, a cost decrease of 20% each year for 10 years does not correspond to a cost decrease of 200%. Let me explain why, using basic math.
When we talk about a decrease of 20%, it means the price is being reduced by 20% of its original value. So, if the original price was $100, a 20% decrease would mean a reduction of $20, making the new price $80 (80% of $100).
Now, if the price is reduced by 20% each year for 10 years, we need to calculate the total decrease. To do this, we can continue applying the 20% decrease to the new price each year.
Year 1: $80 - 20% = $80 - ($80 * 0.2) = $80 - $16 = $64
Year 2: $64 - 20% = $64 - ($64 * 0.2) = $64 - $12.8 = $51.2
Year 3: $51.2 - 20% = $51.2 - ($51.2 * 0.2) = $51.2 - $10.24 = $40.96
We repeat this process for the remaining years until we reach the end of the 10th year. By the end of 10 years, the price will have decreased to approximately $20.83. Therefore, the total decrease in cost over the 10-year period is not 200%, but rather about 79.17%.
So, the cost decrease of 20% per year for 10 years does not result in a total decrease of 200%.