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The population of a hornet nest experienced growth at a 20% monthly rate, compounded
continuously. At the end of a 5 month period, the population reached a size of 815
hornets.
Assuming that every month has 30 days, how many hornets were in the nest at the
beginning of the 5 months according to the exponential growth function? Round your
answer to the nearest whole number, and do not include units.

Respuesta :

Using an exponential function, it is found that at the beginning, there were 328 hornets.

An increasing exponential function has the following format:

[tex]A(t) = A(0)(1 + r)^t[/tex]

In which:

  • A(0) is the initial value.
  • r is the growth rate, as a decimal.

In this problem, there is a growth of 20%, hence [tex]r = 0.2[/tex].

After 5 months, the size is of 815, hence, when [tex]t = 5, A(t) = 815[/tex], and this is used to find A(0).

[tex]A(t) = A(0)(1 + r)^t[/tex]

[tex]815 = A(0)(1 + 0.2)^5[/tex]

[tex]A(0) = \frac{815}{(1.2)^5}[/tex]

[tex]A(0) = 328[/tex]

At the beginning, there were 328 hornets.

A similar problem is given at https://brainly.com/question/22733028

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