# 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?

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### 2 Answers

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