The population of a culture of bacteria Pt where t is time i

The population of a culture of bacteria, P(t), where t is time in days, is growing at a rate that is proportional to the population itself and the growth rate is 0.2. The initial population is 30. What is the population after 20 days? How long does it take for the population to double? ()

Solution

a) i⁶⁰¹= i⁶⁰⁰ . i

since i⁴=1 , i⁶⁰⁰= (i⁴)¹⁵⁰ =(1)¹⁵⁰=1

i⁶⁰¹= i⁶⁰⁰ . i = 1.i =i

b)1/i¹⁷

i¹⁷=i¹⁶.i = 1.i =i

1/i¹⁷= 1/i =-i since 1= -i²