Solve the given problem releated to continuous compounding interest. How long will it take $\$ 1,000$ to triple if it is invested at an annual interest rate of $5.7 \%$ compounded continuously? Round to the nearest year. $\mathrm{yr}$

Step 1 ：We are given that the principal amount (P) is $1000, the amount of money accumulated after n years, including interest (A) is $3000, and the annual interest rate (r) is 5.7% or 0.057 in decimal form. We need to find the time the money is invested for in years (t).

Step 2 ：The formula for continuous compounding interest is \(A = P e^{rt}\).

Step 3 ：We can rearrange this formula to solve for t, giving us \(t = \frac{1}{r} \ln(\frac{A}{P})\).

Step 4 ：Substituting the given values into this formula, we get \(t = \frac{1}{0.057} \ln(\frac{3000}{1000})\).

Step 5 ：Solving this equation gives us \(t \approx 19\).

Step 6 ：So, it will take approximately \(\boxed{19}\) years for the investment to triple.