Reference no: EM131103954
Modeling - Math 056 - Homework 1
1. In class, discussed the Fibonacci problem where Rn represented the number of pairs of rabbits in generation n. Let Nn be the number of newborn pairs in generation (month) n. These were denoted by open circles on our tree in class.
(a) Find the biological meaning of N0 if N0 = 1 and N1 = 1. (Hint: In the model in class, R0 refers to the first month the rabbits were placed in the field.)
(b) Find N2, N3, N4, N5. What do you notice? Write out the model.
(c) Write N2, N3, N4, and N5 as functions of N0 and N1. What do you notice about the coefficients?
2. Run a search for the golden ratio in biology (ex. google). Find three examples where φ shows up in biological phenomena. Choose one of these examples and write a short paragraph explaining the example. Please cite your sources.
3. For the following questions, consider the growth of an aphid population. Use the model developed in class:
an = [fr(1 - m)]na0.
(a) If the fractional mortality of aphids is 80% and the sex ratio (ratio of females to the total number of aphids) is 50%, what minimum fecundity is required to prevent extinction?
(b) Establish a general condition on the fecundity of aphids to guarantee population growth given a fixed survivorship and a known sex ratio.
|
Software with statistical capability
: Magnum Magnetics makes induction meters used in vending machines to test the validity of coins. Their specifications require the induction reading capability of the meters to fall between 0.25 and 0.50 Tesla (T) units. Quality analysts took a ran..
|
|
What is the slope of the budget constraint
: Do you need to know the income of the consumer to answer this question? Why or why not?
|
|
What do insurance industry use experience modification rate
: Summarize briefly the problems most widely associated with workers' compensation. What does the insurance industry use Experience Modification Rate (EMR) to determine?
|
|
National unemployment rate
: Suppose that you have a time series dataset on the monthly U.S. national unemployment rate for the past 40 years. Do you think that unemployment is better characterized as a moving average process,
|
|
What minimum fecundity is required to prevent extinction
: Modeling - Math 056 - Homework 1. Establish a general condition on the fecundity of aphids to guarantee population growth given a fixed survivorship and a known sex ratio
|
|
What is the production possibilities curve
: What is the production possibilities curve and how is it useful? What 4 factors contribute to determining any point in this model? How would we apply this framework to the real world?
|
|
Economic market models
: Disney World has doubled their ticket prices at their amusement parks over the last 10 years, which of the economic market models we covered explains this behavior? Be sure to take into account that competitor parks are nearby. Be sure to detail..
|
|
Dynamic pricing model
: Ride hailing services utilize a dynamic pricing model. Using supply and demand tools (you don't have to actually show the graphs... but they may help you on scratch paper) illustrate how microeconomics explains the shifts in pricing and how it de..
|
|
Compute the speed of the car
: You are in charge of calibrating the radar guns for a local police department. One such device emits microwaves at a frequency of 2.03 GHz. Calculate the speed of the car.
|