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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 a bee hive, and t represents the time in weeks. Based on the model, by approximately what percent does the population of honey bees in a bee hive increase each month? 40.7% 59.3% 26.2% 73.8%. Equation is h(t)=10,015(1.593)t/2

Respuesta :

[tex]\bf \textit{initial amount}\qquad \qquad 10,015\\\\ -------------------------------\\\\ \stackrel{\textit{amount after a week, t = 1}}{h(1)=10015(1.593)^{\frac{1}{2}}}\implies h(1)\approx 12640.34[/tex]

so, from 10015 to 12640.34 the difference is 2625.34, so it increased by 2625.34 bees.

now, if we take 10015 to be the 100%, what is 2625.34 off of it in percentage?

[tex]\bf \begin{array}{ccll} amount&\%\\ \text{\textemdash\textemdash\textemdash}&\text{\textemdash\textemdash\textemdash}\\ 10015&100\\ 2625.34&p \end{array}\implies \cfrac{10015}{2625.34}=\cfrac{100}{p}\implies p=\cfrac{2625.34\cdot 100}{10015}[/tex]
We know that the population of honey bees in a bee hive can be modeled by the following function [tex]h(t)=10,015(1.593) \dfrac{t}{y} [/tex]. 

Where function "h" represents the population of honey bees in a bee hive, and "t" represents the time in weeks.  

[tex]h(t)=10,015(1.593) \frac{t}{2}[/tex]    [tex]t=1[/tex] 

[tex]h(1) = 12640.34[/tex] 

[tex] 12640.34 - 10015 = 2625.34[/tex]     Bees Increases by 

Therefore, 10015 would represent 100% and we can find the percentage of increase or decrease.  

[tex] \dfrac{10015}{2625.34}[/tex] * [tex] \dfrac{100}{p}[/tex]  Cross Multiply 

[tex] \dfrac{2625.34 * 100}{10015}[/tex] 


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