#### Answer

(a) $t=27.73~years$
(b) $t=43.94~years$

#### Work Step by Step

$A=Pe^{rt}~~$ (Continuous compounding)
$A=2500e^{0.025t}$
(a) We want $A=5000$
$5000=2500e^{0.025t}$
$2=e^{0.025t}$
$\ln2=\ln e^{0.025t}$
$\ln2=0.025t$
$t=\frac{\ln2}{0.025}=27.73~years$
(b) We want $A=7500$
$7500=2500e^{0.025t}$
$3=e^{0.025t}$
$\ln3=\ln e^{0.025t}$
$\ln3=0.025t$
$t=\frac{\ln3}{0.025}=43.94~years$