Question

Every minute a computer sends a virus to 5 new computers. The following minute the original computer sends it's virus to 5 be computers, and each computer that received it the 1st minute sends it to 5 more. This pattern continues until someone figures out how to stop it. Write an equation to represent this situation.

Answer 1

initially, you start with 1 computer with the virus
a0=1
after the first minute you have 5 new computers with virus
a1 = a0+a0*5 = a0*6
after the 2nd minute, all those computers (6) will have infected 5 computers each
a2= a1+a1*5 = a1*6
keep going
a3=a2+a2*5 = a2*6 = a1*6*6 = a0*6*6*6= a0*6^3

so it reasons after the nth minute the number of computers infected (an) can be represented as
an= a0 *6^n