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Exponents and Logarithms

A hive of bees contains 27 bees when it is first discovered. After 3 days, there are 36 bees. It is determined that the population of bees increases exponentially.

 

How many bees are will there be after 30 days? Express your answer as an exact value and rounded to the nearest whole number.

 Dec 20, 2019
 #1
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We have the form 

 

P  =  ab^t         where  a = the original population =  27    and t is the number of days

 

So....we have

 

36  = 27b^3      divide both sides  by  27

 

(4/3)  = b^3      take the  3rd root

 

(4/3)^(1/3)  = b     

 

So   we want to find this

 

P  =  27[ *4/3)^(1/3) ] ^30

 

P =  27 (4/3)^10  =  exact value

 

P   ≈  479  bees after 30 days

 

 

cool cool cool

 Dec 20, 2019
edited by CPhill  Dec 20, 2019

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