Answer :
Recall that to calculate the amount after t years that is compounded continously at a intereset rate r of an investment of a principal P is given by the formula
[tex]A=Pe^{rt}[/tex]In this case, the initial amount is P. Since we want to calculate the value of t for which A is exactly 2*P we have the equation
[tex]2P=Pe^{rt}[/tex]we know that r=0.049 and we want to solve this equation for t. WE start by dividing both sides by P. So we get
[tex]2=e^{0.049t}[/tex]If we apply the natural logarithm on both sides, we get
[tex]0.049t=\ln (2)[/tex]so if we divide both sides by 0.049, we get
[tex]t=\frac{\ln (2)}{0.049}=14.14145860[/tex]which rounded to the nearest tenth of a year is 14.1 years