Answer:
Part 1) 
Part 2) 
Step-by-step explanation:
Part 1) we know that
The compound interest formula is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
n is the number of times interest is compounded per year
in this problem we have
substitute in the formula above
Apply log both sides
![log(2)=log[(1.01)^{6t}]](https://tex.z-dn.net/?f=log%282%29%3Dlog%5B%281.01%29%5E%7B6t%7D%5D)
solve for t

Part 2) we know that
The formula to calculate continuously compounded interest is equal to
where
A is the Final Investment Value
P is the Principal amount of money to be invested
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
substitute in the formula above
Apply ln both sides
![ln(2)=ln[(e)^{0.06t}]](https://tex.z-dn.net/?f=ln%282%29%3Dln%5B%28e%29%5E%7B0.06t%7D%5D)

