Answer:
[tex]t=15.4\ years[/tex]
Step-by-step explanation:
The exponential growth function compounded continuously is equal to
[tex]A=P(e)^{rt}[/tex]
where
A is the final population
P is the initial population
r is the rate of growth in decimal
t is Number of years
e is the mathematical constant number
we have
[tex]A=4x\\P=x\\ r=9\%=9/100=0.09[/tex]
substitute in the function above
[tex]4x=x(e)^{0.09t}[/tex]
simplify
[tex]4=(e)^{0.09t}[/tex]
Take natural log of both sides
[tex]ln(4)=ln[(e)^{0.09t}][/tex]
[tex]ln(4)=0.09t(ln(e))[/tex]
[tex]ln(e)=1[/tex]
[tex]ln(4)=0.09t[/tex]
[tex]t=ln(4)/0.09[/tex]
[tex]t=15.4\ years[/tex]
