Rate of Change: Bees in Wildflower Meadow (a-c)

In summary, the conversation discusses the relationship between the number of bees and wildflower plants. Part (a) mentions the number of bees per wildflower plant, while part (b) introduces a mathematical equation to calculate the rate of change of bees with respect to plants. Part (c) raises concerns about the accuracy of the model, specifically in relation to seasonal variations.
  • #1
chwala
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Homework Statement
See attached.
Relevant Equations
differentiation
1686666885968.png


part (a)

The number of Bees per Wildflower plant.

part (b)

##\dfrac{dB}{dF}= \dfrac{dB}{dt} ⋅\dfrac{dt}{dF}####\dfrac{dB}{dF}=\left[\dfrac{2-3\sin 3t}{5e^{0.1t}}\right]##

##\dfrac{dB}{dF} (t=4)= 0.4839##part (c)

For values of ##t>12## The number of Bees per wildflower plants reduces drastically at 3 bees per 10 plants (number of bees are becoming insignificant)...that may not be a true representation of the model.Insight welcome...
 
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  • #2
I haven't checked your numbers, but I don't see anything wrong with your work, otherwise.
 
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  • #3
chwala said:
part (b)
.
##\dfrac{dB}{dF} (t=4)= 0.4839##
You can’t justify giving the answer to four significant figures. The parameters in the equations are only precise to one sig. fig. I'd round to two sig. figs. as a compromise.

chwala said:
part (c)

For values of ##t>12## The number of Bees per wildflower plants reduces drastically at 3 bees per 10 plants (number of bees are becoming insignificant)...that may not be a true representation of the model.
I think what they are getting at is this...

The question states that the data are acquired during a number of weeks over summer. During summer the number of wildflowers can reasonably be expected to steadily increase. But after 12 weeks (t>12) we will have entered autumn and the number of wildflowers will be decreasing. This is not correctly modelled by ##F(t) = e^{0.1t}##.

An improved version of ##F(t)## might include seasonal variations over a complete year.
 
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  • #4
Part a: the rate of change of number of bees with number of plants. Note that dB/dt can be negative, but you don't have negative bees per plant.
 
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