Question

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?

Answer 1

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.

$P=P_0(1+r)^n$

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

$34820=P_0(1+0.78)^5$

$P_0=\dfrac{34820}{(1.78)^5}=1948.63$

$P_0\approx 1949$

Hence, The initial number of bacteria in the culture was 1949