Answer:
360
Step-by-step explanation:
Points to Note
When the beehive was discovered, there were 27 bees
After 3 days, the numbers of bee increased to 36
Progression Type : Exponential (also knows as geometry)
Number of bees after 30 days is unknown
First we need to get the rate of progression (increment or decrement) between the first day and the third day it was discovered
From the question, we have
T1 = 27 ------------- T1 represents number of bees initiallly (1st term)
T2 = 36 ------------- T2 represents 2nd term (number of bees after 3days)
T3 represents 3rd term (after additional 3 days; i.e. 6 days)
T4 represents 4th term (after 12 days)
If you follow this progression, you'll noticed that
T10 = Number of bees on the 30th day
Since, it's an exponential progression; we have to divide to get the rate of progression
R = 36/27 ------------ R represents Rate of progress (also known as common radius)
R = 4/3
Using this progression formula
Tn = aR^(n-1)
Where a = T1 = 1st term = 27
R = Rate of progression = 4/3
n = Number of term = 10
Substituting these values in the progression formula
T10 = 27 * (4/3) ^(10-1)
T10 = 27 * (4/3)^9
T10 = 27 * 262144/19683
T10 = 7077888/19683
T10 = 359.594
T10 = 360 (approximated)
is already in simplest form.