Question

Roberto has been studying a type of bacteria that doubles every month. Originally, there were 3 bacterial cells. He wants to know how many there will be after 43 months. Which equation should he use?

Answer 1

bacteria be  double in every month,
initially, there are only three bacterial cells.
first month ⇒ 3 bacterial cells 
2nd month ⇒ 3 × 2 = 6  bacterial cells
3rd month ⇒ 6 × 2 = 12 bacterial cells 
.........................................
................................
here, we absorbed , bacteria are 3 , 6 , 12 , 24, ..........
do you not think that , number of bacteria is in GP,
where, first term, a = 3 and common ratio, r = 2 
 ∴ nth term = $\bold{a_n=ar^{n-1}}$ 
so, 43th term = $\bold{a_{43}=3(2)^{43-1}}$

hence, option 4 is correct