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