A bacteria gives birth to two new bacteria in each second and the life span of each bacteria is 5 seconds. The process of the reproduction is continuous until the death of the bacteria. initially there is one newly born bacteria at time t = 0, the find the total number of live bacteria just after 10 seconds :

At T=0, there was only 1 bacteria
At T= 1, 1 bacteria gives birth to 2 bacteria so total bacteria become 3
At T=2, each 3 bacteria gives birth to 2 more bacteria... so total bacteria 3*2+3=9 or we can wright it as 3²
At T=3, 3³
At T=4, 3⁴
At T=10, 3¹⁰
Since bacteria die after 5 sec so all the bacteria born from T=0 to T=5 will die at T=10
therefore
3¹⁰-3⁵
3⁵(3⁵-1)
243*(3⁵-1) answer

pls explain in detail like formula wise

completion of first second-> 2 new + 1 old =3
2nd second ->(3*2)6new +3 old =9
3rd second->(9*2)new + 9 old =27
4th second ->(27*2)new + 27 old=81
5th second ->(81*2)new + 81 old – 1(life time completes for 1st bacteria) =242
6th second ->242*2new + 242 old – 2(see born in first second which are new)=724
7th second->724*2new+724old – 6(see born in 2nd second which are new)=2166
8th second->2166*3 – 18 =6480
9th second=>6480*3 – 54 =19386
10th second=>19386*3 – 81*2 =57996

Explain please

how you write (3^10_ 3^5 )
pls expline

After 5 sec the 1st bacteria will die. So in 6th second 81-1=80 bacteria will give birth to two new. Similarly in 7th sec 2 more bacteria which were born in in 1st sec will die.