Answer:
5.78 years
Step-by-step explanation:
we know that
The formula to calculate continuously compounded interest is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the Final amount
P is the amount of money owed
r is the rate of interest in decimal
t is Number of Time Periods
e is the mathematical constant number
we have
[tex]t=?\ years\\ P=\$3,000\\r=19\%=19/100=0.19\\A=\$9,000[/tex]
substitute in the formula above
[tex]9,000=3,000(e)^{0.19t}[/tex]
Solve for t
Simplify
[tex]3=(e)^{0.19t}[/tex]
Apply ln both sides
[tex]ln(3)=ln[(e)^{0.19t}][/tex]
[tex]ln(3)=(0.19t)ln(e)[/tex]
Remember that
[tex]ln(e)=1[/tex]
so
[tex]ln(3)=(0.19t)[/tex]
[tex]t=ln(3)/0.19=5.78\ years[/tex]
