Model warming towards room temperature

A bottle of liquid is removed from a refrigerator into a room at constant $20^\circ$C. Its temperature $\theta$ degrees Celsius after $t$ minutes increases at a rate proportional to $(20-\theta)$. Initially $\theta=10$ and $d\theta/dt=1$ degree Celsius per minute. Set up and solve a differential equation to show that $\theta=20-10e^{-t/10}$. Find the time to reach $15^\circ$C, state the large-$t$ behaviour, and sketch $\theta$ against $t$.