At a temperature of 20 degree C the common amoeba reproduces by splitting in half every 24 hours. If we start with a single amoeba how many...will there be after (a) 8 days, (b) 16 days?
As long as there are sufficient nutrients, the amoeba will grow exponentially, splitting in two every 24 hrs. The equation for exponential growth is x = P B^(t/T), where P is the initial population, B is the factor by which a single elements grow, and T is the time period.
x = 1*2^(t/24)
So a) x = 2^8 = 256 amoeba
b) x = 2^16 = 65536 amoeba
After one day 1 amoeba by splitting in half becomes 2
After 2nd day by splitting into the 2 , the 2 amoeba become 2*2 = 2^2
Similarly after After 3rd day the number of them =4*2 = 8=2^3=2^3.
Generalising, the number of them after n days =2^n
So, after the 8th day, by splitting process the number of amoeba =2^8 = 256
After 16 days the number of amoeba =2^16 = 65536