Q:

A type of organism's cells split every minute. If the organism has 4 cells when the cells begin to split, how many cells will the organism have after 6 minutes?

Accepted Solution

A:
Answer:The total of cells will the organism have after 6 minutes is 252Step-by-step explanation:* Lets consider this problem as a geometric series- There is a constant ratio between each two consecutive numbers Ex: # 5  ,  10  ,  20  ,  40  ,  80  ,  ………………………. (×2) # 5000  ,  1000  ,  200  ,  40  ,  …………………………(÷5) * General term (nth term) of a Geometric series: ∵ U1 = a  ,  U2  = ar  ,  U3  = ar^2  ,  U4 = ar^3  ,  U5 = ar^4 ∴ Un = ar^n-1- Where r is the ratio between each two consecutive terms and  n is the position of the number in the series* The sum of first n terms of a Geometric Progression is calculate from  Sn = a(1 - r^n)/1 - r  - In the problem the cell split every minute- The organism has 4 cells when the cells begin to split∴ a = 4# 4 , 8 , 16 , 32 , .......∴ r = 2- The total of cells will the organism have after 6 minutes can   calculate from the rule of the sum∴ S6 = 4(1 - 2^6)/1 - 2 = 4(1 - 64)/-1 = 4(-63)/-1 = 252 cells