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katrin2010 [14]
3 years ago
5

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

on of bees increases exponentially.
How many bees are will there be after 30 days?
Mathematics
2 answers:
Levart [38]3 years ago
6 0

Answer:

126

Step-by-step explanation:

andrezito [222]3 years ago
6 0

Answer:

<h2>After 30 days, there will be around 542 bees in the hive.</h2>

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.

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