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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kjcdb8er's profile pic

kjcdb8er | Teacher | (Level 1) Associate Educator

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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

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neela's profile pic

neela | High School Teacher | (Level 3) Valedictorian

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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

 

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