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

1,949

Explanation:

Answer 2

The initial number of bacteria in the culture was 1949

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=(34820)/((1.78)^5)=1948.63`

`P_0\approx 1949`

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