Question

The price of a cellular phone declines by 33 percents of its current value every year. At this rate, approximately how many years will it take for the price of a $243 cell phone to reach $72?

Answer 1

Every year, the price of the smartphone is the $67\%$ of the price of the previous year (since we lose the $33\%$, we remain with the $67\%$).

Since $67\%$ can be written as $\frac{67}{100}$, the price after one year will be

$243 \cdot \frac{67}{100} = 162.81$

After two years, the price is the $67\%$ of the price after one year:

$162.81 \cdot \frac{67}{100} = 109.08$

And so on: after three years we have

$109.08 \cdot \frac{67}{100} = 73.08$

So, the answer is somewhere between three and four years.