## College Algebra 7th Edition

(a) $t=\frac{\ln 5}{10\ln\frac{11}{8}}$ (b) $t\approx 0.505391$
(a) We are given: $10(1.375)^{10t}=50$ $10(\frac{11}{8})^{10t}=50$ $(\frac{11}{8})^{10t}=\frac{50}{10}=5$ We take the natural log of both sides and use log rules to simplify: $10t\ln\frac{11}{8}=\ln 5$ $t=\frac{\ln 5}{10\ln\frac{11}{8}}$ (b) We use a calculator to solve: $t\approx 0.505391$