Question

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

Answer 1

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

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?


`\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}`

Answer 2

We know that the population of honey bees in a bee hive can be modeled by the following function
`h(t)=10,015(1.593) (t)/(y)`.

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


`h(t)=10,015(1.593) (t)/(2)`
`t=1`


`h(1) = 12640.34`


`12640.34 - 10015 = 2625.34` Bees Increases by

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


`(10015)/(2625.34)` *
`(100)/(p)` Cross Multiply


`(2625.34 * 100)/(10015)`