Aparticular strain of bacteria doubles in population every 10 minutes. assuming you start with a single bacterium in a petri dish, how many bacteria will there be in 2.5 hours

Let the initial number of bacteria be

Number of bacteria doubles in population every 10 minutes

After 10 minutes number of bacteria = 2

number of bacteria present after t minutes,

When t = 2.5 hrs = 2.5 (60) = 150 minutes

So every 10 minutes t = 150/10 = 15

Now substitute t = 15 minutes and = 1, we get

x = 32,768 bacteria

(n^3 - n)

= n(n-1)(n+1)

since it is divisible by 3 and 2 ,because it is a multiple 3 consecutive number

if, n-1 is odd then n+1 is also odd, then it is a multiple of 9

but if, n-1 is even then n+1 is also even, then it is a multiple of 4

so, largest multiple = max(9*2, 4*3) = max(18, 12) = 18