Mathematics, 09.07.2019 04:40, jessicachichelnitsky
An initial investment of $3 is worth $108 after 5 years. if the annual growth reflects a geometric sequence, approximately how much will the investment be worth after 11 years?
Answers: 1
![\bf \begin{array}{ll} \stackrel{year}{term}&value\\ \cline{1-2} a_1&3\\ a_2&3r\\ a_3&3rr\\ a_4&3rrr\\ a_5&3rrrr\\ &3r^4 \end{array}\qquad \qquad \stackrel{\textit{5th year}}{108}=3r^4\implies \cfrac{108}{3}=r^4\implies 36=r^4 \\\\\\ \sqrt[4]{36}=r\implies \sqrt[4]{6^2}=r\implies 6^{\frac{2}{4}}=r\implies 6^{\frac{1}{2}}=r\implies \sqrt{6}=r](/tpl/images/0068/1625/90364.png)
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