The relative growth rate for a certain type of bacteria population is 78% per hour. A small culture has formed and in just 5 hours the count shows to be 34,820 bacteria in the culture. What is the initial number of bacteria in the culture?

Let us assume the initial number of bacteria in the culture = x

After 1 hour,

The number of bacteria = 185x/100

= 1.85x

After 2 hours,

The number of bacteria = (185 * 1.85x) / 100

= 3.42x

So

3.42x = 12500

x = 12500/3.42

= 3654.97

= 3655

From the above deduction, we can conclude that the initial number of bacteria in the culture is 3655.