Question

The relative growth rate for a certain type of bacteria population is 85% per hour. A small culture has formed and in just 2 hours the count shows to be 12,500 bacteria in the culture. What is the initial number of bacteria in the culture? PLS USE THE FORMULA P(t) = Pe^rt

Answer 1

Let us assume the initial number of bacteria in the culture = xAfter 1 hour,The number of bacteria = 185x/100                                      = 1.85xAfter 2 hours,The number of bacteria = (185 * 1.85x)/100                                       = 3.42xSo3.42x = 12500x = 12500/3.42   = 3654.97   = 3655From the above deduction, we can conclude that the initial number of bacteria in the culture is 3655.

Answer 2

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