Question

you bought a video game for 50$,but it loses 25% of its value every six months. how much will the video game be worth after two years​

Answer 1

There are 4 periods of 6 months in 2 years so 50x0.75^4= $15.82

Answer 2

keeping in mind that two years is 24 months, and we know that cyclically it's losing 25% every 6 months.

$\bf \textit{Periodic/Cyclical Exponential Decay} \\\\ A=P(1 - r)^{\frac{t}{c}}\qquad \begin{cases} A=\textit{accumulated amount}\\ P=\textit{initial amount}\dotfill &50\\ r=rate\to 25\%\to \frac{25}{100}\dotfill &0.25\\ t=\textit{elapsed time}\dotfill &24\\ c=period\dotfill &6 \end{cases} \\\\\\ A=50(1 - 0.25)^{\frac{24}{6}}\implies A=50(0.75)^4\implies A\approx 15.82$