Answer:
The initial number of bacteria in the culture was 1949
Step-by-step explanation:
The relative growth rate for a certain type of bacteria population is 78% per hour.
As we know the growth of bacteria is exponential function.
[tex]P=P_0(1+r)^n[/tex]
where,
P is population of bacteria after n hours.
P₀ is initial population.
r is rate of growth per hour
n is number of hours
A small culture has formed and in just 5 hours the count shows to be 34,820 bacteria in the culture.
P = 34820 , n = 5 , r = 0.78
[tex]34820=P_0(1+0.78)^5[/tex]
[tex]P_0=\dfrac{34820}{(1.78)^5}=1948.63[/tex]
[tex]P_0\approx 1949[/tex]
Hence, The initial number of bacteria in the culture was 1949
