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Delvig [45]
3 years ago
15

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​
Mathematics
2 answers:
kvv77 [185]3 years ago
8 0
There are 4 periods of 6 months in 2 years so 50x0.75^4= $15.82
castortr0y [4]3 years ago
4 0

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

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