3. 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.

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)

the above table 1 will calculate the population size (n) after a certain length of time (t). all you need to do is plug in the initial population number (no), the growth rate (r) and the length of time (t). the constant (e) is already entered into the equation. it stands for the base of the natural logarithms (approximately 2.71828). growth rate (r) and time (t) must be expressed in the same unit of time, such as years, days, hours or minutes. for humans, population growth rate is based on one year. if a population of people grew from 1000 to 1040 in one year, then the percent increase or annual growth rate is 40/1000 x 100 = 4 percent.

step-by-step explanation: