Answer
a) $7328.73$
b) $3.46$ years
Work Step by Step
In $A(t)=Pe^{rt}$ for continuous interest, $P,r,t$ respectively stand for the principal, interest rate per year and the number of years. $A(t)$ is the amount after $t$ years. So if we invest $P=6500$ at an interest rate of $r=0.06$, the amount after $t$ years is:
a) $A(2)=6500e^{0.06(2)}\approx7328.73$
b) In this case: $A=8000$. Then our equation is:
$8000=6500e^{0.06(t)}\\16/13=e^{0.06(t)}\\0.06t=\ln(16/13)\\t=\frac{\ln(16/13)}{0.06}\approx3.46$ years