Question

Next O Post Test: Interpreting, Analyzing, and Building Functions

12
The population of honey bees in a bee hive can be modeled by the following function, where function h represents the population of honey bees in
bee hive, and t represents the time in weeks.
h(t) 10,015(1.593)
Based on the model, by approximately what percent does the population of honey bees in a bee hive increase each month?
OA. 59.3%
OB. 26.2%
OC. 40.7%
OD. 73.8%
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Answer 1

The function given to model the population of honey bees in a bee hive is:

h(t) = 10,015(1.593)^t

Here, t represents the time in weeks.

To find the percentage increase in population per month, we need to find the value of the function after one month and after two months, as there are approximately 4.33 weeks in a month.

After one month (4.33 weeks), we have:

h(4.33) = 10,015(1.593)^4.33

h(4.33) ≈ 10,015(2.288)

h(4.33) ≈ 22,913

After two months (8.66 weeks), we have:

h(8.66) = 10,015(1.593)^8.66

h(8.66) ≈ 10,015(4.155)

h(8.66) ≈ 41,605

The population of honey bees increased from 22,913 to 41,605 in two months, which is an increase of:

(41,605 - 22,913)/22,913 ≈ 81.7%

So, the population of honey bees in a bee hive increases by approximately 81.7% per two months. To find the percentage increase per month, we divide 81.7 by 2:

81.7/2 ≈ 40.85

Therefore, the population of honey bees in a bee hive increases by approximately 40.85% per month.

The closest option to this answer is option (C) 40.7%.