The Leaves of a Tree
"How much do the leaves on a tree weigh?" How might one estimate the actual weight of the leaves (or for that matter any other parts of the tree)? How might one classify leaves? Build a mathematical model to describe and classify leaves. Consider and answer the following:
•Why do leaves have the various shapes that they have?
•Do the shapes “minimize” overlapping individual shadows that are cast, so as to maxi mize exposure? Does the distribution of leaves within the “volume” of the tree and its branches effect the shape?
•Speaking of profiles, is leaf shape (general characteristics) related to tree profile/branching structure?
•How would you estimate the leaf mass of a tree? Is there a correlation between the leaf mass and the size characteristics of the tree (height, mass, volume defined by the profile)?
In addition to your one page summary sheet prepare a one page letter to an editor of a scientific journal outlining your key findings.
Nowadays the heavy metal pollution is so common that people pay more and more attention to it. The aim of this paper is to calculate the maximum of methylmercury in human body during their lifetime and the maximum number of fish the average adult can safely eat per month. From City Officials research[1], we get information thatthemeanvalue of methylmercury in bass samples of the Neversink Reservoir is 1300 ug/kg and the average weight of bass people consume per month is 0.7 kg. According to the different consuming time in every month, we construct a discrete dynamical system model for the amount of methylmercury that will be bioaccumulated in the average adult body.In ideal conditions, we assume people consume bass at fixed term per month. Based on it, we construct fixed-ingestion model and wereach the conclusion that the maximum amount of methylmercury the average adult human will bioaccumulate in their lifetime is 3505 ug. As methylmercury ingestedis not only coming from bass but also from other food, hence, we make further revise to our model so that the model is closer to the actual situation. As a result, we figure out the maximum amount of methylmercury the average adult human will bioaccumulate in their lifetime is 3679 ug. As a matter of fact, although we assume people consume one fish per month, the consuming time has great randomness. Taking the randomness into consideration, we construct a random-ingestion model at the basis of the first model. Through computer simulations, we obtain the maximum of methylmercury in human body is 4261 ug. We also calculate the maximum amount is 4420 ug after random-ingestion model is revised.As
