Question

the price of the phone by x percent each day. You decided to wait until the price dropped to $50.14 on the 16th day to purchase yours. What was the daily percent decrease that the UT Math Department set for the iPhone 3.14? The new iPhone 3.14 is being sold at the UT Math Department. The original price is $1200 (day 0), but they are going to decrease the price of the phone by x percent each day. You decided to wait until the price dropped to $50.14 on the 16th day to purchase yours.
What was the daily percent decrease that the UT Math Department set for the iPhone 3.14?

Answer 1

$\bf \qquad \textit{Amount for Exponential Decay} \\\\ A=P(1 - r)^t\qquad \begin{cases} A=\textit{accumulated amount}\dotfill&50.14\\ P=\textit{initial amount}\dotfill &1200\\ r=rate\to r\%\to \frac{r}{100}\dotfill\\ t=\textit{elapsed time}\dotfill &16\\ \end{cases}$

$\bf 50.14=1200(1-r)^{16}\implies \cfrac{50.14}{1200}=(1-r)^{16}\implies \sqrt[16]{\cfrac{50.14}{1200}}=1-r \\\\\\ r=1-\sqrt[16]{\cfrac{50.14}{1200}}\implies r\approx 0.18\implies \stackrel{\textit{converting to percent}}{r\approx 0.18\cdot 100}\implies r\approx \stackrel{\%}{18}\quad \leftarrow x$