Answer
(a). $t=\frac{-5 \ln ({1-\frac{13I}{60}})}{13},$
(b). $t=0.2185$ seconds
Work Step by Step
$I=\frac{60}{13}\left(1-e^{-13t/5} \right),$
(a).
$\frac{13I}{60}=1-e^{-13t/5},$
$e^{-13t/5}=1-\frac{13I}{60},$
$\frac{-13t}{5}=\ln ({1-\frac{13I}{60}}),$
$t=\frac{-5 \ln ({1-\frac{13I}{60}})}{13},$
(b). for $I=2A,$
$t=\frac{-5 \ln ({1-\frac{26}{60}})}{13},$
$t=\frac{-5 \ln (\frac{60-26}{60})}{13},$
$t=\frac{-5 \ln ({\frac{34}{60}})}{13},$
$t=0.2185$ seconds
