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

• chwala
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.
chwala
Gold Member
Homework Statement
See attached.
Relevant Equations
differentiation

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...

Last edited:
I haven't checked your numbers, but I don't see anything wrong with your work, otherwise.

chwala
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.

chwala
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.

SammyS, chwala and Steve4Physics

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