Answer
(a) $t=\frac{\ln 5}{10\ln\frac{11}{8}}$
(b) $t\approx 0.505391$
Work Step by Step
(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:
$t\approx 0.505391$
