Chapter 11 - Quadratic Functions and Equations - 11.1 Quadratic Equations - 11.1 Exercise Set - Page 707: 78

$8\%$

Work Step by Step

$A=P(1+r)^{t}\qquad$..Substitute $7290$ for $A,\ 6250$ for $P$ and $2$ for $t$. $7290=6250(1+r)^{2}\qquad$..divide both sides by $6250$. $\displaystyle \frac{7290}{6250}=(1+r)^{2}\qquad$..simplify. $\displaystyle \frac{729}{625}=(1+r)^{2}$ According to the general principle of square roots: For any real number $k$ and any algebraic expression $x$ : $\text{If }x^{2}=k,\text{ then }x=\sqrt{k}\text{ or }x=-\sqrt{k}$. $1+r=\pm\sqrt{\frac{729}{625}}\qquad$..add $-1$ to both sides. $1-1+r=\pm\sqrt{\frac{729}{625}}-1\qquad$..simplify. $r=-\displaystyle \frac{25}{25}\pm\frac{27}{25}\qquad$.. The interest rate cannot be negative, we eliminate the negative solution. $r=-\displaystyle \frac{25}{25}+\frac{27}{25}=0.08=8\%$

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