Question

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?

Answer 1

Answer:

After 30 days, there will be around 542 bees in the hive.

Step-by-step explanation:

Givens

• The hive contains 27 bees in first place.
• After 3 days, there are 36 bees.

The population growth is modelled by the expression

$A=A_{0}e^{kt}$

Where $A$ is the population after $t$ days, $A_{0}$ is the initial population, $t$ is days and $k$ is the constant of proportionality.

Basically, in these kind of problems, we use the given information to find $k$ first

$A=A_{0}e^{kt}\\36=27e^{3k}\\\frac{36}{27}= e^{3k}\\ln(\frac{4}{3})=ln(e^{3k})\\3k=ln(\frac{4}{3})\\k\approx 0.10$

Now, with this constant, we find the population of bees after 30 days.

$A=A_{0}e^{kt}\\A=27e^{0.10(30)}\\A=27e^{3}\approx 542$

Therefore, after 30 days, there will be around 542 bees in the hive.