Answer
(a) $t=18.48~years$
(b) $t=29.30~years$
Work Step by Step
$A=Pe^{rt}~~$ (Continuous compounding)
$A=2500e^{0.0375t}$
(a) We want $A=5000$
$5000=2500e^{0.0375t}$
$2=e^{0.0375t}$
$\ln2=\ln e^{0.0375t}$
$\ln2=0.0375t$
$t=\frac{\ln2}{0.0375}=18.48~years$
(b) We want $A=7500$
$7500=2500e^{0.0375t}$
$3=e^{0.0375t}$
$\ln3=\ln e^{0.0375t}$
$\ln3=0.0375t$
$t=\frac{\ln3}{0.0375}=29.30~years$