Please answer the part of designing an algorithm and the alogirthm running time.

There are n bacteria and 1 virus in a Petri dish. Within the first minute, the virus kills one bacterium and produces another copy of itself, and all of the remaining bacteria reproduce, making 2 viruses and 2 * (n-1) bacteria. In the second minute, each of the viruses kills a bacterium and produces a new copy of itself (resulting in 4 viruses and 2 * (2 * (n-1)-2) = 4 * n - 8 bacteria; again, the remaining bacteria reproduce. This process continues every minute. Will the viruses eventually kill all the bacteria? If so, design an algorithm that computes how many steps it will take. How does the running time of your algorithm depend on n?