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

chwala
Gold Member
Messages
2,825
Reaction score
413
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...
 
Last edited:
Physics news on Phys.org
I haven't checked your numbers, but I don't see anything wrong with your work, otherwise.
 
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.
 
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.
 
  • Like
Likes SammyS, chwala and Steve4Physics
There are two things I don't understand about this problem. First, when finding the nth root of a number, there should in theory be n solutions. However, the formula produces n+1 roots. Here is how. The first root is simply ##\left(r\right)^{\left(\frac{1}{n}\right)}##. Then you multiply this first root by n additional expressions given by the formula, as you go through k=0,1,...n-1. So you end up with n+1 roots, which cannot be correct. Let me illustrate what I mean. For this...
Back
Top