2. The world population is approximately 6.1 billion, and can be modeled by the function $\mathrm{P}(t)=6.1 e^{0.012 t}$ where population is measured in billions and time $t$ is measured in years. How long will it take for the world population to double? Round answer to the nearesî tenth.

Step 1 ：The problem is asking for the time it will take for the world population to double. This means we need to solve the equation \(6.1e^{0.012t} = 2*6.1\) for \(t\).

Step 2 ：This is a simple exponential growth problem, and we can solve it by taking the natural logarithm of both sides and then solving for \(t\).

Step 3 ：Let's denote the initial population as \(P0 = 6.1\), the growth rate as \(r = 0.012\), and the final population as \(P = 12.2\).

Step 4 ：Solving for \(t\), we get \(t = 57.76226504666211\).

Step 5 ：Rounding to the nearest tenth, we get \(t = 57.8\).

Step 6 ：Final Answer: It will take approximately \(\boxed{57.8}\) years for the world population to double.