Chapter 4, Exponential and Logarithmic Functions - Section 4.5 - Exponential and Logarithmic Functions - 4.5 Exercises - Page 405: 91

$t=6.325~years$

$A=P(1+\frac{r}{n})^{nt}$ $r=7.5$% $=0.075$ $P=5000$ $A=8000$ $8000=5000(1+\frac{0.075}{4})^{4t}$ $1.6=(1+\frac{0.075}{4})^{4t}$ $\log1.6=\log(1+\frac{0.075}{4})^{4t}$ $\log1.6=4t[\log(1+\frac{0.075}{4})]$ $t=\frac{\log1.6}{4\log(1+\frac{0.075}{4})}=6.325$